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Label Class Equation Sato-Tate \(\overline{\Q}\)-simple \(\GL_2\) Rank*
504.a.27216.1 504.a \(y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21\) $G_{3,3}$ 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
529.a.529.1 529.a \(y^2 + (x^3 + x + 1)y = -x^5\) $G_{3,3}$ 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
574.a.293888.1 574.a \(y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1\) $\mathrm{USp}(4)$ 0
576.a.576.1 576.a \(y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x\) $E_2$ 0
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
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
597.a.597.1 597.a \(y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x\) $\mathrm{USp}(4)$ 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
600.b.450000.1 600.b \(y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45\) $G_{3,3}$ 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
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.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
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
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.704512.1 688.a \(y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1\) $\mathrm{USp}(4)$ 0
688.a.704512.2 688.a \(y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1\) $\mathrm{USp}(4)$ 0
691.a.691.1 691.a \(y^2 + (x + 1)y = x^5 - x^3 - x^2\) $\mathrm{USp}(4)$ 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
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
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
720.a.6480.1 720.a \(y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5\) $G_{3,3}$ 0
720.b.116640.1 720.b \(y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90\) $G_{3,3}$ 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
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
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