Results (50 matches)

Label Class Conductor Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Equation
256.a.512.1 256.a $$2^{8}$$ $0$ $\Z/2\Z\oplus\Z/10\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$
400.a.409600.1 400.a $$2^{4} \cdot 5^{2}$$ $0$ $\Z/3\Z\oplus\Z/6\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^6 + 4x^4 + 4x^2 + 1$
576.a.576.1 576.a $$2^{6} \cdot 3^{2}$$ $0$ $\Z/10\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$
576.b.147456.1 576.b $$2^{6} \cdot 3^{2}$$ $0$ $\Z/4\Z\oplus\Z/4\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^6 + 2x^4 + 2x^2 + 1$
1152.a.147456.1 1152.a $$2^{7} \cdot 3^{2}$$ $0$ $\Z/8\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^6 - 2x^4 + 2x^2 - 1$
1600.b.409600.1 1600.b $$2^{6} \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^6 - 4x^4 + 4x^2 - 1$
2304.b.147456.1 2304.b $$2^{8} \cdot 3^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = -x^6 - 2x^4 - 2x^2 - 1$
4096.e.524288.1 4096.e $$2^{12}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - 2x^4 - 2x^2 - x$
4608.a.4608.1 4608.a $$2^{9} \cdot 3^{2}$$ $0$ $\Z/4\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + x^3y = x^4 + 2x^2 + 2$
4608.b.4608.1 4608.b $$2^{9} \cdot 3^{2}$$ $0$ $\Z/4\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + x^3y = -x^4 + 2x^2 - 2$
4608.c.27648.1 4608.c $$2^{9} \cdot 3^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - x^4 + x^2 - x$
6400.b.12800.1 6400.b $$2^{8} \cdot 5^{2}$$ $0$ $\Z/6\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + x^3y = 2x^4 + 4x^2 + 2$
6400.d.12800.1 6400.d $$2^{8} \cdot 5^{2}$$ $1$ $\Z/6\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + x^3y = -2x^4 + 4x^2 - 2$
6400.f.64000.1 6400.f $$2^{8} \cdot 5^{2}$$ $2$ $\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + x^3y = -2x^4 - 3x^3 + x^2 + 6x + 4$
6400.g.64000.1 6400.g $$2^{8} \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^3 + x^2 + x + 1)y = -x^6 - x^3 - x - 1$
6400.i.409600.1 6400.i $$2^{8} \cdot 5^{2}$$ $0$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = -x^6 - 4x^4 - 4x^2 - 1$
8192.a.32768.1 8192.a $$2^{13}$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - 3x^3 + 2x$
8192.b.131072.1 8192.b $$2^{13}$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - 3x^4 + 6x^2 - 4x$
9216.a.36864.1 9216.a $$2^{10} \cdot 3^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 + x^3 + x$
12544.d.25088.1 12544.d $$2^{8} \cdot 7^{2}$$ $2$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^3 + x^2 + x + 1)y = x^4 - x^3 + x^2 - x$
12544.g.175616.1 12544.g $$2^{8} \cdot 7^{2}$$ $1$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + x^3y = x^5 + x^4 - 2x^2 - 4x - 2$
12800.c.128000.1 12800.c $$2^{9} \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - 3x^4 + 3x^2 - x$
16384.a.32768.1 16384.a $$2^{14}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 + 3x^3 + 2x$
25600.a.102400.1 25600.a $$2^{10} \cdot 5^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - 3x^3 + x$
25600.d.128000.1 25600.d $$2^{10} \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 + x^4 + x^2 - x$
25600.e.128000.1 25600.e $$2^{10} \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - x^4 - x^2 - x$
36864.b.36864.1 36864.b $$2^{12} \cdot 3^{2}$$ $1$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - x^3 + x$
69696.c.627264.1 69696.c $$2^{6} \cdot 3^{2} \cdot 11^{2}$$ $0$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^3 + x^2 + x + 1)y = x^6 + 3x^4 - x^3 + 3x^2 - x + 1$
73728.c.884736.1 73728.c $$2^{13} \cdot 3^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 + 5x^3 + 6x$
73728.d.884736.1 73728.d $$2^{13} \cdot 3^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = 2x^5 - 5x^3 + 3x$
78400.a.78400.1 78400.a $$2^{6} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^3 + x^2 + x + 1)y = -x^6 - 3x^4 - x^3 - 3x^2 - x - 1$
102400.b.102400.1 102400.b $$2^{12} \cdot 5^{2}$$ $1$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - x^3 - x$
102400.e.102400.1 102400.e $$2^{12} \cdot 5^{2}$$ $0$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 + 3x^3 + x$
135424.l.270848.1 135424.l $$2^{8} \cdot 23^{2}$$ $0$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^3 + x^2 + x + 1)y = -x^6 - 2x^4 - x^3 - 2x^2 - x - 1$
147456.c.884736.1 147456.c $$2^{14} \cdot 3^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = 2x^5 + 5x^3 + 3x$
147456.e.884736.1 147456.e $$2^{14} \cdot 3^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - 5x^3 + 6x$
193600.d.968000.1 193600.d $$2^{6} \cdot 5^{2} \cdot 11^{2}$$ $0$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^3 + x^2 + x + 1)y = -x^6 - x^4 - x^3 - x^2 - x - 1$
193600.e.968000.1 193600.e $$2^{6} \cdot 5^{2} \cdot 11^{2}$$ $2$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^3 + x^2 + x + 1)y = 2x^4 - x^3 + 2x^2 - x$
262144.a.262144.1 262144.a $$2^{18}$$ $1$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - 2x^3 - x$
262144.b.524288.1 262144.b $$2^{18}$$ $1$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 + 2x^3 + 2x$
262144.c.524288.1 262144.c $$2^{18}$$ $1$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - 2x^3 + 2x$
278784.a.557568.1 278784.a $$2^{8} \cdot 3^{2} \cdot 11^{2}$$ $0$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + y = 6x^6 - 8x^4 + 4x^2 - 1$
278784.b.557568.1 278784.b $$2^{8} \cdot 3^{2} \cdot 11^{2}$$ $1$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + y = -6x^6 - 8x^4 - 4x^2 - 1$
331776.e.995328.1 331776.e $$2^{12} \cdot 3^{4}$$ $0$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 + 3x^3 + 3x$
331776.g.995328.1 331776.g $$2^{12} \cdot 3^{4}$$ $1$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - 3x^3 + 3x$
589824.a.589824.1 589824.a $$2^{16} \cdot 3^{2}$$ $0$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - 4x^3 + x$
589824.b.589824.1 589824.b $$2^{16} \cdot 3^{2}$$ $2$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 + 4x^3 + x$
692224.a.692224.1 692224.a $$2^{12} \cdot 13^{2}$$ $0$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - 3x^3 - x$
778752.b.778752.1 778752.b $$2^{9} \cdot 3^{2} \cdot 13^{2}$$ $2$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + y = 6x^6 - 10x^4 + 5x^2 - 1$
778752.c.778752.1 778752.c $$2^{9} \cdot 3^{2} \cdot 13^{2}$$ $2$ $\Z/2\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + y = -6x^6 - 10x^4 - 5x^2 - 1$