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Label Class Equation Sato-Tate \(\overline{\Q}\)-simple \(\GL_2\) Rank*
196.a.21952.1 196.a \(y^2 + (x^2 + x)y = x^6 + 3x^5 + 6x^4 + 7x^3 + 6x^2 + 3x + 1\) $E_1$ 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.8232.1 294.a \(y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14\) $G_{3,3}$ 0
360.a.6480.1 360.a \(y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5\) $G_{3,3}$ 0
363.a.11979.1 363.a \(y^2 + (x^2 + 1)y = x^5 + 2x^3 + 4x^2 + 2x\) $G_{3,3}$ 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
394.a.3152.1 394.a \(y^2 + (x + 1)y = -x^5\) $\mathrm{USp}(4)$ 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
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
450.a.36450.1 450.a \(y^2 + (x^3 + 1)y = x^5 - 4x^4 - 9x^3 + 28x^2 - 6x - 16\) $G_{3,3}$ 0
464.a.29696.1 464.a \(y^2 + (x + 1)y = 8x^5 + 3x^4 - 4x^3 - 2x^2\) $\mathrm{USp}(4)$ 0
464.a.29696.2 464.a \(y^2 + xy = 4x^5 + 33x^4 + 72x^3 + 16x^2 + x\) $\mathrm{USp}(4)$ 0
472.a.60416.1 472.a \(y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2\) $\mathrm{USp}(4)$ 0
484.a.1936.1 484.a \(y^2 + y = x^6 + 2x^4 + x^2\) $G_{3,3}$ 0
504.a.27216.1 504.a \(y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21\) $G_{3,3}$ 0
555.a.8325.1 555.a \(y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x\) $\mathrm{USp}(4)$ 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
588.a.18816.1 588.a \(y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8\) $G_{3,3}$ 0
600.a.18000.1 600.a \(y^2 + xy = 10x^5 - 18x^4 + 8x^3 + x^2 - x\) $G_{3,3}$ 0
600.a.96000.1 600.a \(y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2\) $G_{3,3}$ 0
600.b.30000.1 600.b \(y^2 + (x^3 + x)y = x^4 + x^2 - 3\) $G_{3,3}$ 0
604.a.9664.1 604.a \(y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21\) $\mathrm{USp}(4)$ 0
604.a.9664.2 604.a \(y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x\) $\mathrm{USp}(4)$ 0
630.a.34020.1 630.a \(y^2 + (x^2 + x)y = 3x^5 + 10x^4 - 23x^2 - 6x + 15\) $G_{3,3}$ 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.2576.1 644.a \(y^2 + (x^2 + x)y = -5x^6 + 11x^5 - 20x^4 + 20x^3 - 20x^2 + 11x - 5\) $G_{3,3}$ 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
676.a.5408.1 676.a \(y^2 + (x^3 + x^2 + x)y = x^3 + 3x^2 + 3x + 1\) $G_{3,3}$ 0
676.b.17576.1 676.b \(y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1\) $E_1$ 0
688.a.2752.1 688.a \(y^2 + y = 2x^5 - 5x^4 + 4x^3 - x\) $\mathrm{USp}(4)$ 0
704.a.45056.1 704.a \(y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2\) $\mathrm{USp}(4)$ 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
720.a.6480.1 720.a \(y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5\) $G_{3,3}$ 0
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
741.a.28899.1 741.a \(y^2 + (x + 1)y = -3x^5 - x^4 + 2x^2 + x\) $\mathrm{USp}(4)$ 0
762.a.3048.1 762.a \(y^2 + (x^3 + x^2 + x)y = x^2 + x + 1\) $\mathrm{USp}(4)$ 0
762.a.82296.1 762.a \(y^2 + (x^2 + x)y = x^5 - 8x^4 + 14x^3 + 2x^2 - x\) $\mathrm{USp}(4)$ 0
768.a.1536.1 768.a \(y^2 + y = 2x^5 - x^4 - 3x^3 + x\) $\mathrm{USp}(4)$ 0
768.a.4608.1 768.a \(y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2 - x - 1\) $\mathrm{USp}(4)$ 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.12544.1 784.b \(y^2 + (x^3 + x)y = -1\) $G_{3,3}$ 0
784.b.25088.1 784.b \(y^2 + (x^2 + 1)y = -x^6 - 3x^5 + 7x^4 + 2x^3 - 49x^2 + 41x - 9\) $G_{3,3}$ 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
807.a.2421.1 807.a \(y^2 + (x^3 + x)y = x^5 - 2x^3 - x^2 + 2x - 1\) $\mathrm{USp}(4)$ 0
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