LMFDB - Elliptic curve search results

Refine search

Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

		Sort order	Select

Results (28 matches)

Download displayed columns for results to

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
6240.l2	6240g1	6240.l	6240g	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$384$	$-0.390813$	$1560896/975$	$0.86761$	$2.10782$	$[0, -1, 0, 10, 0]$	$y^2=x^3-x^2+10x$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[]$
6240.bc2	6240q1	6240.bc	6240q	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.398573777$	$1$	$3$	$384$	$-0.390813$	$1560896/975$	$0.86761$	$2.10782$	$[0, 1, 0, 10, 0]$	$y^2=x^3+x^2+10x$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(9, 30)]$
12480.i2	12480bw1	12480.i	12480bw	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{12} \cdot 3 \cdot 5^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.166687727$	$1$	$5$	$1536$	$-0.044240$	$1560896/975$	$0.86761$	$2.39385$	$[0, -1, 0, 39, -39]$	$y^2=x^3-x^2+39x-39$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(5, 16)]$
12480.cg2	12480cs1	12480.cg	12480cs	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{12} \cdot 3 \cdot 5^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$1536$	$-0.044240$	$1560896/975$	$0.86761$	$2.39385$	$[0, 1, 0, 39, 39]$	$y^2=x^3+x^2+39x+39$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[]$
18720.f2	18720be1	18720.f	18720be	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3^{7} \cdot 5^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.602344903$	$1$	$7$	$3072$	$0.158493$	$1560896/975$	$0.86761$	$2.54249$	$[0, 0, 0, 87, 88]$	$y^2=x^3+87x+88$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(8, 36)]$
18720.q2	18720bd1	18720.q	18720bd	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3^{7} \cdot 5^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.057555667$	$1$	$5$	$3072$	$0.158493$	$1560896/975$	$0.86761$	$2.54249$	$[0, 0, 0, 87, -88]$	$y^2=x^3+87x-88$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(4, 18)]$
31200.t2	31200bn1	31200.t	31200bn	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{6} \cdot 3 \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.795944037$	$1$	$5$	$9216$	$0.413906$	$1560896/975$	$0.86761$	$2.71316$	$[0, -1, 0, 242, -488]$	$y^2=x^3-x^2+242x-488$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(3, 16)]$
31200.bq2	31200ce1	31200.bq	31200ce	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{6} \cdot 3 \cdot 5^{8} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$9216$	$0.413906$	$1560896/975$	$0.86761$	$2.71316$	$[0, 1, 0, 242, 488]$	$y^2=x^3+x^2+242x+488$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[]$
37440.dv2	37440fu1	37440.dv	37440fu	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{12} \cdot 3^{7} \cdot 5^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$0.819023476$	$1$	$7$	$12288$	$0.505067$	$1560896/975$	$0.86761$	$2.77007$	$[0, 0, 0, 348, 704]$	$y^2=x^3+348x+704$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(10, 72)]$
37440.fc2	37440fr1	37440.fc	37440fr	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{12} \cdot 3^{7} \cdot 5^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.022995338$	$1$	$5$	$12288$	$0.505067$	$1560896/975$	$0.86761$	$2.77007$	$[0, 0, 0, 348, -704]$	$y^2=x^3+348x-704$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(6, 40)]$
62400.bq2	62400eg1	62400.bq	62400eg	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{12} \cdot 3 \cdot 5^{8} \cdot 13 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$3.042401378$	$1$	$11$	$36864$	$0.760479$	$1560896/975$	$0.86761$	$2.91950$	$[0, -1, 0, 967, 2937]$	$y^2=x^3-x^2+967x+2937$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(7, 100), (157, 2000)]$
62400.gq2	62400gi1	62400.gq	62400gi	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{12} \cdot 3 \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$3.324472231$	$1$	$1$	$36864$	$0.760479$	$1560896/975$	$0.86761$	$2.91950$	$[0, 1, 0, 967, -2937]$	$y^2=x^3+x^2+967x-2937$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(237/2, 4125/2)]$
81120.f2	81120bc1	81120.f	81120bc	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{6} \cdot 3 \cdot 5^{2} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$64512$	$0.891662$	$1560896/975$	$0.86761$	$2.99100$	$[0, -1, 0, 1634, 6616]$	$y^2=x^3-x^2+1634x+6616$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[]$
81120.bk2	81120bq1	81120.bk	81120bq	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{6} \cdot 3 \cdot 5^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$7.815532577$	$1$	$1$	$64512$	$0.891662$	$1560896/975$	$0.86761$	$2.99100$	$[0, 1, 0, 1634, -6616]$	$y^2=x^3+x^2+1634x-6616$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(925/7, 60696/7)]$
93600.bp2	93600br1	93600.bp	93600br	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{6} \cdot 3^{7} \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$3.288579076$	$1$	$3$	$73728$	$0.963212$	$1560896/975$	$0.86761$	$3.02862$	$[0, 0, 0, 2175, -11000]$	$y^2=x^3+2175x-11000$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(165, 2200)]$
93600.dq2	93600bn1	93600.dq	93600bn	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{6} \cdot 3^{7} \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.680347200$	$1$	$5$	$73728$	$0.963212$	$1560896/975$	$0.86761$	$3.02862$	$[0, 0, 0, 2175, 11000]$	$y^2=x^3+2175x+11000$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(20, 250)]$
162240.dr2	162240cz1	162240.dr	162240cz	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{12} \cdot 3 \cdot 5^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.399877531$	$1$	$3$	$258048$	$1.238235$	$1560896/975$	$0.86761$	$3.16485$	$[0, -1, 0, 6535, -59463]$	$y^2=x^3-x^2+6535x-59463$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(1179, 40560)]$
162240.gu2	162240g1	162240.gu	162240g	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{12} \cdot 3 \cdot 5^{2} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$258048$	$1.238235$	$1560896/975$	$0.86761$	$3.16485$	$[0, 1, 0, 6535, 59463]$	$y^2=x^3+x^2+6535x+59463$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[]$
187200.eg2	187200dj1	187200.eg	187200dj	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{12} \cdot 3^{7} \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.213321438$	$1$	$7$	$294912$	$1.309786$	$1560896/975$	$0.86761$	$3.19827$	$[0, 0, 0, 8700, -88000]$	$y^2=x^3+8700x-88000$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(85, 1125)]$
187200.md2	187200fo1	187200.md	187200fo	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{12} \cdot 3^{7} \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.576219674$	$1$	$5$	$294912$	$1.309786$	$1560896/975$	$0.86761$	$3.19827$	$[0, 0, 0, 8700, 88000]$	$y^2=x^3+8700x+88000$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(26, 576)]$
243360.dj2	243360dj1	243360.dj	243360dj	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{6} \cdot 3^{7} \cdot 5^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.428773436$	$1$	$5$	$516096$	$1.440968$	$1560896/975$	$0.86761$	$3.25754$	$[0, 0, 0, 14703, -193336]$	$y^2=x^3+14703x-193336$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(43, 720)]$
243360.eu2	243360eu1	243360.eu	243360eu	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{6} \cdot 3^{7} \cdot 5^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$7.030674782$	$1$	$1$	$516096$	$1.440968$	$1560896/975$	$0.86761$	$3.25754$	$[0, 0, 0, 14703, 193336]$	$y^2=x^3+14703x+193336$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(404/5, 82458/5)]$
305760.z2	305760z1	305760.z	305760z	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 $	$ - 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{6} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$3.113830388$	$1$	$5$	$138240$	$0.582142$	$1560896/975$	$0.86761$	$2.38272$	$[0, -1, 0, 474, 960]$	$y^2=x^3-x^2+474x+960$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(-1, 22)]$
305760.ey2	305760ey1	305760.ey	305760ey	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 $	$ - 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{6} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$138240$	$0.582142$	$1560896/975$	$0.86761$	$2.38272$	$[0, 1, 0, 474, -960]$	$y^2=x^3+x^2+474x-960$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[]$
405600.bf2	405600bf1	405600.bf	405600bf	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{6} \cdot 3 \cdot 5^{8} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$3.225790754$	$1$	$5$	$1548288$	$1.696381$	$1560896/975$	$0.86761$	$3.36603$	$[0, -1, 0, 40842, -908688]$	$y^2=x^3-x^2+40842x-908688$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(191, 3718)]$
405600.ga2	405600ga1	405600.ga	405600ga	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{6} \cdot 3 \cdot 5^{8} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$1548288$	$1.696381$	$1560896/975$	$0.86761$	$3.36603$	$[0, 1, 0, 40842, 908688]$	$y^2=x^3+x^2+40842x+908688$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[]$
486720.cj2	486720cj1	486720.cj	486720cj	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{12} \cdot 3^{7} \cdot 5^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.106542053$	$1$	$7$	$2064384$	$1.787540$	$1560896/975$	$0.86761$	$3.40270$	$[0, 0, 0, 58812, -1546688]$	$y^2=x^3+58812x-1546688$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(156, 3380)]$
486720.ga2	486720ga1	486720.ga	486720ga	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{12} \cdot 3^{7} \cdot 5^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$0.990214058$	$1$	$7$	$2064384$	$1.787540$	$1560896/975$	$0.86761$	$3.40270$	$[0, 0, 0, 58812, 1546688]$	$y^2=x^3+58812x+1546688$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[(13, 1521)]$

Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (28 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Learn more

Refine search Advanced search options

Results (28 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Refine search