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Label Class Equation Sato-Tate \(\overline{\Q}\)-simple \(\GL_2\) Rank*
249.a.249.1 249.a \(y^2 + (x^3 + 1)y = x^2 + x\) $\mathrm{USp}(4)$ 0
249.a.6723.1 249.a \(y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2\) $\mathrm{USp}(4)$ 0
294.a.294.1 294.a \(y^2 + (x^3 + 1)y = x^4 + x^2\) $G_{3,3}$ 0
294.a.8232.1 294.a \(y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14\) $G_{3,3}$ 0
295.a.295.1 295.a \(y^2 + (x^3 + 1)y = -x^2\) $\mathrm{USp}(4)$ 0
295.a.295.2 295.a \(y^2 + (x^2 + x + 1)y = x^5 - 40x^3 + 22x^2 + 389x - 608\) $\mathrm{USp}(4)$ 0
363.a.43923.1 363.a \(y^2 + x^2y = 11x^5 - 13x^4 - 7x^3 + 10x^2 + x - 2\) $G_{3,3}$ 0
389.a.389.1 389.a \(y^2 + (x^3 + x)y = x^5 - 2x^4 - 8x^3 + 16x + 7\) $\mathrm{USp}(4)$ 0
389.a.389.2 389.a \(y^2 + (x + 1)y = x^5 + 2x^4 + 2x^3 + x^2\) $\mathrm{USp}(4)$ 0
394.a.394.1 394.a \(y^2 + (x^3 + x)y = 2x^5 + x^4 - 12x^3 + 17x - 9\) $\mathrm{USp}(4)$ 0
394.a.3152.1 394.a \(y^2 + (x + 1)y = -x^5\) $\mathrm{USp}(4)$ 0
400.a.409600.1 400.a \(y^2 = x^6 + 4x^4 + 4x^2 + 1\) $E_1$ 0
427.a.2989.1 427.a \(y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4\) $\mathrm{USp}(4)$ 0
448.a.448.2 448.a \(y^2 + (x^3 + x)y = -2x^4 + 7\) $N(G_{1,3})$ 0
448.a.448.1 448.a \(y^2 + (x^3 + x)y = x^4 - 7\) $N(G_{1,3})$ 0
450.a.2700.1 450.a \(y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x\) $G_{3,3}$ 0
464.a.464.1 464.a \(y^2 + (x + 1)y = -x^6 - 2x^5 - 2x^4 - x^3\) $\mathrm{USp}(4)$ 0
472.a.60416.1 472.a \(y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2\) $\mathrm{USp}(4)$ 0
476.a.952.1 476.a \(y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54\) $G_{3,3}$ 0
523.a.523.1 523.a \(y^2 + (x + 1)y = x^5 - x^4 - x^3\) $\mathrm{USp}(4)$ 0
523.a.523.2 523.a \(y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x\) $\mathrm{USp}(4)$ 0
576.a.576.1 576.a \(y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x\) $E_2$ 0
578.a.2312.1 578.a \(y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x\) $G_{3,3}$ 0
587.a.587.1 587.a \(y^2 + (x^3 + x + 1)y = -x^2 - x\) $\mathrm{USp}(4)$ 1
588.a.18816.1 588.a \(y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8\) $G_{3,3}$ 0
603.a.603.1 603.a \(y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x\) $\mathrm{USp}(4)$ 0
603.a.603.2 603.a \(y^2 + (x^2 + 1)y = x^5 - x^3 + x\) $\mathrm{USp}(4)$ 0
640.a.81920.1 640.a \(y^2 + x^3y = 3x^4 + 13x^2 + 20\) $N(G_{1,3})$ 0
640.a.81920.2 640.a \(y^2 + x^3y = -3x^4 + 13x^2 - 20\) $N(G_{1,3})$ 0
644.a.659456.1 644.a \(y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3\) $G_{3,3}$ 0
644.b.14812.1 644.b \(y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1\) $\mathrm{USp}(4)$ 0
686.a.686.1 686.a \(y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x\) $N(G_{1,3})$ 0
688.a.2752.1 688.a \(y^2 + y = 2x^5 - 5x^4 + 4x^3 - x\) $\mathrm{USp}(4)$ 0
688.a.704512.2 688.a \(y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1\) $\mathrm{USp}(4)$ 0
688.a.704512.1 688.a \(y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1\) $\mathrm{USp}(4)$ 0
691.a.691.1 691.a \(y^2 + (x + 1)y = x^5 - x^3 - x^2\) $\mathrm{USp}(4)$ 0
708.a.2832.1 708.a \(y^2 + (x^2 + x + 1)y = x^5\) $\mathrm{USp}(4)$ 0
708.a.19116.1 708.a \(y^2 + (x^3 + 1)y = -x^5 + 4x^2 + 4x - 1\) $\mathrm{USp}(4)$ 0
709.a.709.1 709.a \(y^2 + xy = x^5 - 2x^2 + x\) $\mathrm{USp}(4)$ 0
713.a.713.1 713.a \(y^2 + (x^3 + x + 1)y = -x^5 - x\) $\mathrm{USp}(4)$ 1
726.a.1452.1 726.a \(y^2 + (x^2 + 1)y = 2x^5 + 2x^4 + 6x^3 - 2x^2 - x\) $G_{3,3}$ 0
731.a.12427.1 731.a \(y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3\) $\mathrm{USp}(4)$ 0
743.a.743.1 743.a \(y^2 + (x^3 + x + 1)y = -x^4 + x^2\) $\mathrm{USp}(4)$ 1
762.a.3048.1 762.a \(y^2 + (x^3 + x^2 + x)y = x^2 + x + 1\) $\mathrm{USp}(4)$ 0
763.a.763.1 763.a \(y^2 + (x^3 + x)y = -2x^4 + 2x^2 - x\) $\mathrm{USp}(4)$ 0
784.a.1568.1 784.a \(y^2 + (x^3 + x)y = -2x^4 + 3x^2 - 2\) $G_{3,3}$ 0
784.a.43904.1 784.a \(y^2 + (x^3 + x)y = 4x^4 + 27x^2 + 56\) $G_{3,3}$ 0
784.b.76832.1 784.b \(y^2 + (x + 1)y = -x^6 + 4x^5 - 4x^4 - 2x^3 + 10x - 9\) $G_{3,3}$ 0
800.a.1600.1 800.a \(y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^2\) $G_{3,3}$ 0
800.a.8000.1 800.a \(y^2 + (x^3 + x^2 + x + 1)y = -x^6 + 2x^4 + 4x^3 + 2x^2 - 1\) $G_{3,3}$ 0
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