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Label Class Equation Sato-Tate \(\overline{\Q}\)-simple \(\GL_2\) Rank*
256.a.512.1 256.a \(y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x\) $E_4$ $0$
324.a.648.1 324.a \(y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2\) $E_3$ $0$
388.a.776.1 388.a \(y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x\) $\mathrm{USp}(4)$ $0$
472.a.944.1 472.a \(y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x\) $\mathrm{USp}(4)$ $0$
476.a.952.1 476.a \(y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54\) $\mathrm{SU}(2)\times\mathrm{SU}(2)$ $0$
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 \(y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x\) $\mathrm{USp}(4)$ $0$
529.a.529.1 529.a \(y^2 + (x^3 + x + 1)y = -x^5\) $\mathrm{SU}(2)\times\mathrm{SU}(2)$ $0$
576.a.576.1 576.a \(y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x\) $E_2$ $0$
587.a.587.1 587.a \(y^2 + (x^3 + x + 1)y = -x^2 - x\) $\mathrm{USp}(4)$ $1$
597.a.597.1 597.a \(y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x\) $\mathrm{USp}(4)$ $0$
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 \(y^2 + (x^2 + 1)y = x^5 - x^3 + x\) $\mathrm{USp}(4)$ $0$
686.a.686.1 686.a \(y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x\) $N(\mathrm{U}(1)\times\mathrm{SU}(2))$ $0$
691.a.691.1 691.a \(y^2 + (x + 1)y = x^5 - x^3 - x^2\) $\mathrm{USp}(4)$ $0$
709.a.709.1 709.a \(y^2 + xy = x^5 - 2x^2 + x\) $\mathrm{USp}(4)$ $0$
713.a.713.1 713.a \(y^2 + (x^3 + x + 1)y = -x^5 - x\) $\mathrm{USp}(4)$ $1$
713.b.713.1 713.b \(y^2 + (x^3 + x + 1)y = -x^4\) $\mathrm{USp}(4)$ $0$
743.a.743.1 743.a \(y^2 + (x^3 + x + 1)y = -x^4 + x^2\) $\mathrm{USp}(4)$ $1$
745.a.745.1 745.a \(y^2 + (x^3 + x + 1)y = -x\) $\mathrm{USp}(4)$ $0$
763.a.763.1 763.a \(y^2 + (x^3 + x)y = -2x^4 + 2x^2 - x\) $\mathrm{USp}(4)$ $0$
797.a.797.1 797.a \(y^2 + y = x^5 - x^4 + x^3\) $\mathrm{USp}(4)$ $0$
832.a.832.1 832.a \(y^2 + (x^3 + x)y = x^5 - x^3 + x^2 + 2x - 1\) $\mathrm{USp}(4)$ $0$
841.a.841.1 841.a \(y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 3x^2 + x + 2\) $\mathrm{SU}(2)\times\mathrm{SU}(2)$ $0$
847.a.847.1 847.a \(y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2\) $\mathrm{SU}(2)\times\mathrm{SU}(2)$ $1$
847.d.847.1 847.d \(y^2 + (x^3 + x^2 + x + 1)y = -12x^6 - 15x^5 + 9x^4 + 31x^3 + 9x^2 - 15x - 12\) $\mathrm{SU}(2)\times\mathrm{SU}(2)$ $0$
862.a.862.1 862.a \(y^2 + (x^3 + 1)y = x^5 - 2x^4 - 7x^3 + 7x^2 + 2x + 5\) $\mathrm{USp}(4)$ $0$
862.b.862.1 862.b \(y^2 + (x^3 + x)y = -2x^4 + 3x^2 - x - 1\) $\mathrm{USp}(4)$ $0$
893.a.893.1 893.a \(y^2 + (x^3 + x + 1)y = -x^4 - x^2\) $\mathrm{USp}(4)$ $1$
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 \(y^2 + (x + 1)y = -x^5 + 2x^4 - x^3 - x^2\) $\mathrm{USp}(4)$ $0$
930.a.930.1 930.a \(y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15\) $\mathrm{SU}(2)\times\mathrm{SU}(2)$ $0$
953.a.953.1 953.a \(y^2 + (x^3 + x + 1)y = x^3 + x^2\) $\mathrm{USp}(4)$ $1$
961.a.961.1 961.a \(y^2 + (x^3 + x + 1)y = -x^6 - x^5 - 7x^4 + 74x^3 - 145x^2 + 99x - 33\) $\mathrm{SU}(2)\times\mathrm{SU}(2)$ $0$
961.a.961.2 961.a \(y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 8x^4 + 12x^3 - 18x^2 + 12x - 7\) $\mathrm{SU}(2)\times\mathrm{SU}(2)$ $0$
961.a.961.3 961.a \(y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3 - x - 1\) $\mathrm{SU}(2)\times\mathrm{SU}(2)$ $0$
971.a.971.1 971.a \(y^2 + y = x^5 - 2x^3 + x\) $\mathrm{USp}(4)$ $1$
997.a.997.1 997.a \(y^2 + xy = x^5 - 8x^4 + 16x^3 - x\) $\mathrm{USp}(4)$ $0$
997.a.997.2 997.a \(y^2 + (x + 1)y = x^5 + x^4\) $\mathrm{USp}(4)$ $0$
997.b.997.1 997.b \(y^2 + y = x^5 - 2x^4 + 2x^3 - x^2\) $\mathrm{USp}(4)$ $1$
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