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Label Class Equation Sato-Tate \(\overline{\Q}\)-simple \(\GL_2\) Rank*
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
256.a.512.1 256.a \(y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x\) $E_4$ 0
336.a.172032.1 336.a \(y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56\) $G_{3,3}$ 0
363.a.11979.1 363.a \(y^2 + (x^2 + 1)y = x^5 + 2x^3 + 4x^2 + 2x\) $G_{3,3}$ 0
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
464.a.29696.1 464.a \(y^2 + (x + 1)y = 8x^5 + 3x^4 - 4x^3 - 2x^2\) $\mathrm{USp}(4)$ 0
464.a.29696.2 464.a \(y^2 + xy = 4x^5 + 33x^4 + 72x^3 + 16x^2 + x\) $\mathrm{USp}(4)$ 0
472.a.944.1 472.a \(y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x\) $\mathrm{USp}(4)$ 0
504.a.27216.1 504.a \(y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21\) $G_{3,3}$ 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.b.147456.1 576.b \(y^2 = x^6 + 2x^4 + 2x^2 + 1\) $E_1$ 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
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
704.a.45056.1 704.a \(y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2\) $\mathrm{USp}(4)$ 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
741.a.28899.1 741.a \(y^2 + (x + 1)y = -3x^5 - x^4 + 2x^2 + x\) $\mathrm{USp}(4)$ 0
762.a.82296.1 762.a \(y^2 + (x^2 + x)y = x^5 - 8x^4 + 14x^3 + 2x^2 - x\) $\mathrm{USp}(4)$ 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.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.c.614656.1 784.c \(y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x\) $E_3$ 0
816.a.13872.1 816.a \(y^2 + (x^3 + x^2)y = -2x^4 + 6x^2 - 8x + 3\) $\mathrm{USp}(4)$ 0
816.b.52224.1 816.b \(y^2 + (x^3 + x)y = -x^6 - 12x^4 - 27x^2 - 17\) $G_{3,3}$ 0
826.a.11564.1 826.a \(y^2 + (x^2 + x)y = x^5 + x^4 + 3x^3 - 4x^2 - 4x + 3\) $\mathrm{USp}(4)$ 0
830.a.830000.1 830.a \(y^2 + (x^2 + x)y = x^5 - 2x^4 + 16x^3 + 8x^2 + x\) $\mathrm{USp}(4)$ 0
856.a.1712.1 856.a \(y^2 + (x^3 + x)y = -x^4 - x^3 + x\) $\mathrm{USp}(4)$ 0
862.a.6896.1 862.a \(y^2 + (x^2 + x)y = 4x^5 + 6x^4 - 3x^2 - x\) $\mathrm{USp}(4)$ 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
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
909.a.8181.1 909.a \(y^2 + xy = 3x^5 - 7x^4 + x^3 + 6x^2 - 3x\) $\mathrm{USp}(4)$ 0
925.a.23125.1 925.a \(y^2 + xy = 5x^5 + x^4 - 19x^3 + 18x^2 - 5x\) $\mathrm{USp}(4)$ 0
930.a.930.1 930.a \(y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15\) $G_{3,3}$ 0
960.a.245760.1 960.a \(y^2 = 2x^5 + x^4 + 4x^3 + x^2 + 2x\) $G_{3,3}$ 0
960.a.368640.1 960.a \(y^2 = x^5 + 13x^4 + 44x^3 + 13x^2 + x\) $G_{3,3}$ 0
960.a.983040.1 960.a \(y^2 = x^5 - 2x^4 - x^3 - 2x^2 + x\) $G_{3,3}$ 0
966.a.834624.1 966.a \(y^2 + (x^2 + x)y = x^5 - x^4 + x^3 + x^2 - x + 1\) $\mathrm{USp}(4)$ 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
990.a.8910.1 990.a \(y^2 + (x^2 + x)y = 3x^5 + 4x^4 + 7x^3 + 4x^2 + 3x\) $G_{3,3}$ 0
990.a.240570.1 990.a \(y^2 + (x^2 + x)y = 3x^5 + 28x^4 + 72x^3 + 28x^2 + 3x\) $G_{3,3}$ 0
997.a.997.1 997.a \(y^2 + xy = x^5 - 8x^4 + 16x^3 - x\) $\mathrm{USp}(4)$ 0
1008.a.27216.1 1008.a \(y^2 + (x^3 + x)y = -4x^4 + 15x^2 - 21\) $G_{3,3}$ 0
1051.b.1051.2 1051.b \(y^2 + xy = x^5 + 8x^4 + 16x^3 + x\) $\mathrm{USp}(4)$ 0
1062.a.6372.1 1062.a \(y^2 + (x^3 + 1)y = x^5 - x^4 + x^2 - x\) $\mathrm{USp}(4)$ 1
1070.a.2140.1 1070.a \(y^2 + (x^3 + 1)y = x^3 - x\) $\mathrm{USp}(4)$ 1
1077.a.1077.2 1077.a \(y^2 + (x^3 + 1)y = x^4 + x^3 + 2x^2 + x\) $\mathrm{USp}(4)$ 1
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