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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
249.a.6723.1 249.a \(y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2\) $\mathrm{USp}(4)$ 0
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
360.a.6480.1 360.a \(y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5\) $G_{3,3}$ 0
388.a.776.1 388.a \(y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x\) $\mathrm{USp}(4)$ 0
394.a.3152.1 394.a \(y^2 + (x + 1)y = -x^5\) $\mathrm{USp}(4)$ 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
574.a.293888.1 574.a \(y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1\) $\mathrm{USp}(4)$ 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.b.450000.1 600.b \(y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45\) $G_{3,3}$ 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
688.a.2752.1 688.a \(y^2 + y = 2x^5 - 5x^4 + 4x^3 - x\) $\mathrm{USp}(4)$ 0
800.a.409600.1 800.a \(y^2 = x^6 - 2x^2 + 1\) $G_{3,3}$ 0
816.a.39168.1 816.a \(y^2 + (x^2 + 1)y = 3x^5 - 4x^3 - x^2 + x\) $\mathrm{USp}(4)$ 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
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
1083.a.1083.1 1083.a \(y^2 + (x^3 + x^2 + x + 1)y = -x^3\) $G_{3,3}$ 1
1145.a.143125.1 1145.a \(y^2 + (x^3 + x^2 + x)y = 2x^4 + 4x^3 + 9x^2 + 10x + 9\) $\mathrm{USp}(4)$ 1
1192.a.19072.1 1192.a \(y^2 + (x^3 + x)y = x^3 - 2x^2 - x + 1\) $\mathrm{USp}(4)$ 0
1253.b.1253.1 1253.b \(y^2 + (x^3 + x + 1)y = x^4 + x^2\) $\mathrm{USp}(4)$ 1
1300.a.130000.1 1300.a \(y^2 + (x^3 + x)y = 2x^4 + 9x^2 + 13\) $G_{3,3}$ 1
1312.a.2624.1 1312.a \(y^2 + (x + 1)y = x^6 + 2x^5 + 3x^4 + 2x^3 + x^2\) $\mathrm{USp}(4)$ 1
1312.c.671744.1 1312.c \(y^2 + (x + 1)y = x^6 + 4x^5 + 7x^4 + 5x^3 + 2x^2\) $\mathrm{USp}(4)$ 0
1331.a.1331.1 1331.a \(y^2 + x^3y = -x^4 - x^3 + 2x^2 + 3x + 1\) $N(G_{1,3})$ 1
1338.a.2676.1 1338.a \(y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 2x^2 + x + 1\) $\mathrm{USp}(4)$ 1
1369.a.1369.1 1369.a \(y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^3 - x^2\) $G_{3,3}$ 1
1490.a.1490.1 1490.a \(y^2 + (x^3 + 1)y = x^5 - 4x^3 - 2x^2 + 2x\) $\mathrm{USp}(4)$ 1
1519.a.1519.1 1519.a \(y^2 + (x^3 + x + 1)y = -2x^4 + 2x^2 - x - 1\) $\mathrm{USp}(4)$ 1
1573.a.190333.1 1573.a \(y^2 + x^3y = -7x^4 - 7x^3 + 38x^2 + 21x - 83\) $G_{3,3}$ 1
1647.a.1647.1 1647.a \(y^2 + (x^3 + x + 1)y = x^5\) $\mathrm{USp}(4)$ 1
1655.a.206875.1 1655.a \(y^2 + (x^3 + 1)y = x^5 - x^4 - 7x^3 + 2x^2 + 14x - 10\) $\mathrm{USp}(4)$ 1
1689.a.45603.1 1689.a \(y^2 + (x^2 + x + 1)y = x^5 - 6x^4 + 21x^3 + 15x^2 + 3x\) $\mathrm{USp}(4)$ 1
1753.a.1753.1 1753.a \(y^2 + (x^3 + 1)y = x^2\) $\mathrm{USp}(4)$ 1
1776.b.191808.1 1776.b \(y^2 + y = 2x^5 + x^4 - x^2\) $\mathrm{USp}(4)$ 0
1777.a.1777.1 1777.a \(y^2 + (x^3 + x + 1)y = -3x^4 + 7x^2 - x - 8\) $\mathrm{USp}(4)$ 1
1861.a.1861.1 1861.a \(y^2 + (x^3 + x + 1)y = -x^4 + x^3 - x^2\) $\mathrm{USp}(4)$ 1
1863.a.1863.1 1863.a \(y^2 + (x^3 + x + 1)y = 2x^5 + 4x^4 - 5x^2 + x\) $\mathrm{USp}(4)$ 1
1904.a.487424.1 1904.a \(y^2 + (x^3 + x)y = x^5 - 2x^2 - x + 1\) $\mathrm{USp}(4)$ 0
1908.a.183168.1 1908.a \(y^2 + (x^3 + 1)y = 2x^4 + 3x^3 + 4x^2 + 2x\) $\mathrm{USp}(4)$ 0
1923.b.17307.1 1923.b \(y^2 + (x^3 + x + 1)y = x^4 + 3x^2 + x + 2\) $\mathrm{USp}(4)$ 1
1936.a.1936.1 1936.a \(y^2 + y = -x^6 + 2x^4 - x^2\) $G_{3,3}$ 1
1973.a.1973.1 1973.a \(y^2 + y = x^6 - x^5 + x^2 - x\) $\mathrm{USp}(4)$ 1
1985.a.1985.1 1985.a \(y^2 + (x^3 + 1)y = x^5 + x^4 - x\) $\mathrm{USp}(4)$ 1
1987.a.1987.1 1987.a \(y^2 + (x^3 + x + 1)y = -x^4 + x^2 - x - 1\) $\mathrm{USp}(4)$ 1
2001.a.2001.1 2001.a \(y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3\) $\mathrm{USp}(4)$ 1
2007.a.6021.1 2007.a \(y^2 + (x^2 + x + 1)y = x^6 + x^4\) $\mathrm{USp}(4)$ 1
2020.a.646400.1 2020.a \(y^2 + x^3y = 2x^4 - x^3 + 5x^2 - 4x + 4\) $\mathrm{USp}(4)$ 1
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