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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
256.a.512.1 256.a \(y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x\) $E_4$ 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
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
448.a.448.2 448.a \(y^2 + (x^3 + x)y = -2x^4 + 7\) $N(G_{1,3})$ 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
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
600.b.450000.1 600.b \(y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45\) $G_{3,3}$ 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
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
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
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
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
784.c.614656.1 784.c \(y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x\) $E_3$ 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
800.a.409600.1 800.a \(y^2 = x^6 - 2x^2 + 1\) $G_{3,3}$ 0
810.a.196830.1 810.a \(y^2 + (x + 1)y = x^5 + 15x^4 + 20x^3 - 297x^2 + 94x - 8\) $N(G_{1,3})$ 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.b.9317.1 847.b \(y^2 + (x^2 + 1)y = x^5 + 2x^4 - 3x^3 + 2x^2 - x\) $G_{3,3}$ 0
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