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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
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
400.a.409600.1 400.a \(y^2 = x^6 + 4x^4 + 4x^2 + 1\) $E_1$ 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
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
784.c.614656.1 784.c \(y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x\) $E_3$ 0
1152.a.147456.1 1152.a \(y^2 = x^6 - 2x^4 + 2x^2 - 1\) $J(E_1)$ 0
1296.a.20736.1 1296.a \(y^2 = x^5 - x^4 - 3x^3 + 4x^2 - x\) $E_3$ 0
1600.b.409600.1 1600.b \(y^2 = x^6 - 4x^4 + 4x^2 - 1\) $J(E_1)$ 0
2187.a.6561.1 2187.a \(y^2 + (x^3 + 1)y = -1\) $J(E_3)$ 0
2304.b.147456.1 2304.b \(y^2 = -x^6 - 2x^4 - 2x^2 - 1\) $E_1$ 0
2500.a.50000.1 2500.a \(y^2 + (x^3 + 1)y = x^5 + 2x^3 + x\) $J(E_1)$ 0
2500.a.400000.1 2500.a \(y^2 + (x^3 + 1)y = -2x^6 - 2x^5 + 2x^3 - 2x - 2\) $J(E_1)$ 0
2704.a.43264.1 2704.a \(y^2 = x^5 - 5x^3 - 5x^2 - x\) $E_6$ 0
2916.a.5832.1 2916.a \(y^2 + (x^3 + 1)y = x^3\) $J(E_1)$ 0
2916.a.139968.1 2916.a \(y^2 + (x^2 + x + 1)y = x^6 - 3x^5 + 5x^4 - 6x^3 + x\) $J(E_1)$ 0
3721.a.3721.1 3721.a \(y^2 + (x^3 + x + 1)y = -x^4 + x^3 + 3x^2 + x\) $E_6$ 2
3969.b.35721.1 3969.b \(y^2 + (x^3 + x + 1)y = -2x^5 + 3x^4 - 3x^2\) $E_6$ 2
3969.c.35721.1 3969.c \(y^2 + (x^2 + x)y = x^5 - 5x^4 + 4x^3 - x\) $E_6$ 0
3969.d.250047.1 3969.d \(y^2 + (x^2 + x + 1)y = -3x^5 + 5x^4 - 4x^3 + x\) $J(E_1)$ 0
4096.e.524288.1 4096.e \(y^2 = x^5 - 2x^4 - 2x^2 - x\) $E_4$ 0
4608.a.4608.1 4608.a \(y^2 + x^3y = x^4 + 2x^2 + 2\) $J(E_1)$ 0
4608.b.4608.1 4608.b \(y^2 + x^3y = -x^4 + 2x^2 - 2\) $J(E_1)$ 0
4608.c.27648.1 4608.c \(y^2 = x^5 - x^4 + x^2 - x\) $J(E_4)$ 0
4608.c.884736.1 4608.c \(y^2 = 2x^5 + 7x^4 - 2x^3 - 13x^2 + 10x - 2\) $J(E_4)$ 0
4608.c.884736.2 4608.c \(y^2 = 2x^5 - 7x^4 - 2x^3 + 13x^2 + 10x + 2\) $J(E_4)$ 0
6075.a.18225.1 6075.a \(y^2 + (x^3 + 1)y = x^3 + 1\) $J(E_6)$ 0
6400.b.12800.1 6400.b \(y^2 + x^3y = 2x^4 + 4x^2 + 2\) $J(E_1)$ 0
6400.d.12800.1 6400.d \(y^2 + x^3y = -2x^4 + 4x^2 - 2\) $J(E_1)$ 1
6400.f.64000.1 6400.f \(y^2 + x^3y = -2x^4 - 3x^3 + x^2 + 6x + 4\) $E_4$ 2
6400.g.64000.1 6400.g \(y^2 + (x^3 + x^2 + x + 1)y = -x^6 - x^3 - x - 1\) $E_4$ 0
6400.i.409600.1 6400.i \(y^2 = -x^6 - 4x^4 - 4x^2 - 1\) $E_1$ 0
8192.a.32768.1 8192.a \(y^2 = x^5 - 3x^3 + 2x\) $J(E_4)$ 0
8192.a.131072.1 8192.a \(y^2 + y = 4x^5 + 15x^4 + 8x^3 - 3x^2 - x\) $J(E_4)$ 0
8192.b.131072.1 8192.b \(y^2 = x^5 - 3x^4 + 6x^2 - 4x\) $J(E_2)$ 0
8281.b.405769.1 8281.b \(y^2 + (x^3 + x + 1)y = -3x^5 + 9x^4 - 7x^3 - 2x^2 + x\) $E_6$ 2
8281.c.405769.1 8281.c \(y^2 + (x^2 + x)y = x^5 + 8x^4 + 11x^3 + 3x^2 - x\) $E_6$ 0
8649.b.700569.1 8649.b \(y^2 + (x^2 + x)y = 9x^5 + 2x^4 - 21x^3 - 22x^2 - 8x - 1\) $E_6$ 0
8649.c.700569.1 8649.c \(y^2 + (x^2 + x)y = x^5 + 9x^4 + 13x^3 + 4x^2 - x\) $E_6$ 0
9216.a.36864.1 9216.a \(y^2 = x^5 + x^3 + x\) $J(E_1)$ 0
11881.a.11881.1 11881.a \(y^2 + (x^2 + x)y = x^5 - 3x^4 + 2x^2 - x\) $E_6$ 0
12321.a.36963.1 12321.a \(y^2 + (x^3 + x + 1)y = x^5 + 3x^4 + 4x^3 + 2x^2\) $E_6$ 2
12544.a.12544.1 12544.a \(y^2 = x^5 + 2x^4 - x^3 - 3x^2 - x\) $E_6$ 0
12544.c.12544.1 12544.c \(y^2 = x^5 - 2x^4 - x^3 + 3x^2 - x\) $E_6$ 0
12544.d.25088.1 12544.d \(y^2 + (x^3 + x^2 + x + 1)y = x^4 - x^3 + x^2 - x\) $E_4$ 2
12544.g.175616.1 12544.g \(y^2 + x^3y = x^5 + x^4 - 2x^2 - 4x - 2\) $J(E_4)$ 1
12544.i.614656.1 12544.i \(y^2 = x^5 + 4x^4 - 13x^3 + 9x^2 - x\) $E_3$ 0
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