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Label Class Equation Sato-Tate \(\overline{\Q}\)-simple \(\GL_2\) Rank*
169.a.169.1 169.a \(y^2 + (x^3 + x + 1)y = x^5 + x^4\) $E_6$ 0
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
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
324.a.648.1 324.a \(y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2\) $E_3$ 0
336.a.172032.1 336.a \(y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56\) $G_{3,3}$ 0
353.a.353.1 353.a \(y^2 + (x^3 + x + 1)y = x^2\) $\mathrm{USp}(4)$ 0
388.a.776.1 388.a \(y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x\) $\mathrm{USp}(4)$ 0
400.a.409600.1 400.a \(y^2 = x^6 + 4x^4 + 4x^2 + 1\) $E_1$ 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
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
504.a.27216.1 504.a \(y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21\) $G_{3,3}$ 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
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
640.a.81920.1 640.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
672.a.172032.1 672.a \(y^2 + (x^3 + x)y = -x^6 - 16x^4 - 75x^2 + 56\) $G_{3,3}$ 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.a.562432.1 676.a \(y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x\) $G_{3,3}$ 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
708.a.181248.1 708.a \(y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36\) $\mathrm{USp}(4)$ 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
720.a.6480.1 720.a \(y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5\) $G_{3,3}$ 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
762.a.3048.1 762.a \(y^2 + (x^3 + x^2 + x)y = x^2 + x + 1\) $\mathrm{USp}(4)$ 0
784.a.43904.1 784.a \(y^2 + (x^3 + x)y = 4x^4 + 27x^2 + 56\) $G_{3,3}$ 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
816.b.52224.1 816.b \(y^2 + (x^3 + x)y = -x^6 - 12x^4 - 27x^2 - 17\) $G_{3,3}$ 0
841.a.841.1 841.a \(y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 3x^2 + x + 2\) $G_{3,3}$ 0
847.a.847.1 847.a \(y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2\) $G_{3,3}$ 1
847.d.847.1 847.d \(y^2 + (x^3 + x^2 + x + 1)y = -12x^6 - 15x^5 + 9x^4 + 31x^3 + 9x^2 - 15x - 12\) $G_{3,3}$ 0
847.d.456533.1 847.d \(y^2 + y = -x^6 - 9x^5 - 22x^4 + 3x^3 + 37x^2 - 24x + 4\) $G_{3,3}$ 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
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
882.a.302526.1 882.a \(y^2 + (x^3 + 1)y = x^5 - 2x^4 - 5x^3 + 11x^2 - 12x + 5\) $G_{3,3}$ 0
893.a.893.1 893.a \(y^2 + (x^3 + x + 1)y = -x^4 - x^2\) $\mathrm{USp}(4)$ 1
932.a.3728.1 932.a \(y^2 + y = x^6 - 2x^5 + x^4 + x^2 - x\) $\mathrm{USp}(4)$ 1
936.a.1872.1 936.a \(y^2 + (x^3 + x)y = -x^6 - 9x^4 - 32x^2 - 39\) $G_{3,3}$ 0
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