*20PRESENT: DENNY CHIN, CHRISTOPHER F. DRONEY, Circuit Judges, EDWARD R. KORMAN, Senior District Judge.*
SUMMARY ORDER
Defendants-appellants Alwar Pouryan and Oded Orbach appeal from judgments entered September 26,2013 and December 31, 2013, respectively, following a bench trial, convicting them of providing material support to terrorists and conspiring to acquire and transfer anti-aircraft missiles, in violation of 18 U.S.C. §§ 2339A, 2332g, and 3238. The district court sentenced Pour-yan and Orbach each to concurrent terms of imprisonment of fifteen and twenty-five years. On appeal, both defendants argue that their waiver of a jury trial was ineffective. Pouryan further argues that (1) the evidence was insufficient to support the district court’s verdict and (2) the district court impermissibly shifted the burden of proof to the defense. We assume the parties’ familiarity -with the underlying facts, the procedural history of this case, and the issues on appeal.
1. Jury Trial Waiver
We review the adequacy of a jury trial waiver de novo. United States v. Carmenate, 544 F.3d 105, 107 (2d Cir.2008). An effective waiver must be knowing, voluntary, and intelligent. Id. While the district court is not constitutionally required to go beyond a written waiver, we have recommended a colloquy on the record, specifically “informing] each defendant that a jury is composed of twelve members of the community, that the defendant may participate in the selection of the jurors, that the jury’s verdict must be unanimous, and that a judge alone will decide guilt or innocence if the defendant waives the right to a jury trial.” Id. at 107-08 (quoting Marone v. United States, 10 F.3d 65, 68 (2d Cir. 1993)); Fed.R.Crim.P. 23(a).
The district court found that defendants’ waivers were knowing, voluntary, and intelligent. On March 28, 2013, each defendant signed an effective written waiver, which was reviewed by the district court during a pre-trial conference the same day. Further, the district court conducted a colloquy with both defendants during the pre-trial conference, substantially similar to our suggested colloquy in Carménate. We agree that these were sufficient waivers.
2. Sufficiency of the Evidence
We review a claim of insufficient evidence de novo. United States v. Rangotan, 464 F.3d 321, 324 (2d Cir.2006). We examine the evidence in the light most favorable to the government, see United States v. Jones, 393 F.3d 107, 111 (2d Cir.2004), and uphold a judgment of conviction if “any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” United States v. Coplan, 703 F.3d 46, 62 (2d Cir.2012) (quoting Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979)).
The evidence at trial established that Pouryan actively negotiated with confidential sources posing as Taliban representatives to sell military-grade weapons for use against U.S. military forces. The government presented extensive audio and video recordings of meetings and phone calls between Pouryan and confidential sources, as well as electronic correspondence between defendants, showing that *21Pouryan was attempting to sell weapons, including surface-to-air missiles. On appeal, Pouryan argues that this evidence was insufficient to establish criminal intent, in light of his testimony that he participated in the negotiations solely to collect information for the United States government. We reject this argument. The district court assessed Pouryan’s testimony and determined it was not credible based on detailed findings contradicting his theory, including his failure to report such information prior to his arrest. Based on this evidence, a rational trier of fact could certainly have found the essential elements of the crimes beyond a reasonable doubt.
3. Burden of Proof
Finally, Pouryan argues that the district court impermissibly shifted the burden of proof by requiring him to establish a lack of criminal intent. We disagree. As discussed above, the district court evaluated the government’s evidence and concluded that “standing alone, the recorded and documentary evidence is proof beyond a reasonable doubt of the two charged conspiracies.” App. at 1323-24. Only after considering the government’s evidence did the district court turn to Pouryan’s testimony to assess his defense theory— lack of criminal intent. The district court was entitled to assess the credibility of Pouryan’s testimony alongside the government’s evidence to make a factual determination on intent. See, e.g., Brown v. United States, 356 U.S. 148, 154, 78 S.Ct. 622, 2 L.Ed.2d 589 (1958) (where defendant “takes the stand and testifies in his own defense his credibility may be impeached and his testimony assailed like that of any other witness”); Mallette v. Scully, 752 F.2d 26, 31 (2d Cir.1984) (stating that “it is the trier of fact that weighs the evidence, determines credibility and draws inferences from historic to ultimate facts”); United States v. Zambardi, 276 F.2d 169, 170 (2d Cir.1960) (“The resolution of this conflicting testimony necessarily turned upon an assessment of credibility and thus was a matter for the trial court sitting as trier of fact.”). Accordingly, the burden of proof was not impermissibly shifted to Pouryan.
We have reviewed defendants’ remaining arguments and conclude they are without merit. Accordingly, we AFFIRM the judgment of the district court.
The Honorable Edward R. Korman, of the United States District Court for the Eastern District of New York, sitting by designation.