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Label Class Equation Sato-Tate \(\overline{\Q}\)-simple \(\GL_2\) Rank*
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
353.a.353.1 353.a \(y^2 + (x^3 + x + 1)y = x^2\) $\mathrm{USp}(4)$ 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
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
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
476.a.952.1 476.a \(y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54\) $G_{3,3}$ 0
484.a.1936.1 484.a \(y^2 + y = x^6 + 2x^4 + x^2\) $G_{3,3}$ 0
523.a.523.1 523.a \(y^2 + (x + 1)y = x^5 - x^4 - x^3\) $\mathrm{USp}(4)$ 0
529.a.529.1 529.a \(y^2 + (x^3 + x + 1)y = -x^5\) $G_{3,3}$ 0
576.a.576.1 576.a \(y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x\) $E_2$ 0
576.b.147456.1 576.b \(y^2 = x^6 + 2x^4 + 2x^2 + 1\) $E_1$ 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
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
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
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.81920.2 640.a \(y^2 + x^3y = -3x^4 + 13x^2 - 20\) $N(G_{1,3})$ 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.562432.1 676.a \(y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x\) $G_{3,3}$ 0
688.a.704512.2 688.a \(y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1\) $\mathrm{USp}(4)$ 0
691.a.691.1 691.a \(y^2 + (x + 1)y = x^5 - x^3 - x^2\) $\mathrm{USp}(4)$ 0
708.a.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.b.713.1 713.b \(y^2 + (x^3 + x + 1)y = -x^4\) $\mathrm{USp}(4)$ 0
720.b.116640.1 720.b \(y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90\) $G_{3,3}$ 0
731.a.12427.1 731.a \(y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3\) $\mathrm{USp}(4)$ 0
745.a.745.1 745.a \(y^2 + (x^3 + x + 1)y = -x\) $\mathrm{USp}(4)$ 0
762.a.3048.1 762.a \(y^2 + (x^3 + x^2 + x)y = x^2 + x + 1\) $\mathrm{USp}(4)$ 0
763.a.763.1 763.a \(y^2 + (x^3 + x)y = -2x^4 + 2x^2 - x\) $\mathrm{USp}(4)$ 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.b.12544.1 784.b \(y^2 + (x^3 + x)y = -1\) $G_{3,3}$ 0
800.a.1600.1 800.a \(y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^2\) $G_{3,3}$ 0
807.a.2421.1 807.a \(y^2 + (x^3 + x)y = x^5 - 2x^3 - x^2 + 2x - 1\) $\mathrm{USp}(4)$ 0
816.a.13872.1 816.a \(y^2 + (x^3 + x^2)y = -2x^4 + 6x^2 - 8x + 3\) $\mathrm{USp}(4)$ 0
864.a.1728.1 864.a \(y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^2\) $N(G_{1,3})$ 0
864.a.221184.1 864.a \(y^2 + x^3y = x^5 - 4x^4 - 6x^3 + 33x^2 - 36x + 12\) $N(G_{1,3})$ 0
864.a.442368.1 864.a \(y^2 = x^6 - 4x^4 + 6x^2 - 3\) $N(G_{1,3})$ 0
882.a.63504.1 882.a \(y^2 + (x^2 + x)y = x^5 + x^4 + x^3 + 3x^2 + 3x + 1\) $G_{3,3}$ 0
909.a.909.1 909.a \(y^2 + (x^3 + x)y = -x^4 + x^2 - x\) $\mathrm{USp}(4)$ 0
925.a.925.1 925.a \(y^2 + (x + 1)y = -x^5 + 2x^4 - x^3 - x^2\) $\mathrm{USp}(4)$ 0
968.a.234256.1 968.a \(y^2 + x^3y = 6x^4 + 47x^2 + 121\) $G_{3,3}$ 1
970.a.1940.1 970.a \(y^2 + (x + 1)y = x^5 + x^4 + x^3 + x^2\) $\mathrm{USp}(4)$ 0
975.a.63375.1 975.a \(y^2 + (x^3 + 1)y = -x^5 + x^3 + 2x^2 + x - 1\) $\mathrm{USp}(4)$ 0
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