LMFDB - Elliptic curve search results

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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	Manin constant

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Results (24 matches)

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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	Manin constant
2057.c1	2057a1	2057.c	2057a	$1$	$1$	$ 11^{2} \cdot 17 $	$ - 11^{3} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1.040968105$	$1$	$2$	$360$	$-0.006020$	$4096000/4913$	$0.90722$	$2.94788$	$[0, -1, 1, 37, 76]$	$y^2+y=x^3-x^2+37x+76$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(4, 16)]$	$1$
2057.d1	2057b1	2057.d	2057b	$1$	$1$	$ 11^{2} \cdot 17 $	$ - 11^{9} \cdot 17^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1$	$1$	$0$	$3960$	$1.192928$	$4096000/4913$	$0.90722$	$4.83375$	$[0, -1, 1, 4437, -119285]$	$y^2+y=x^3-x^2+4437x-119285$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[ ]$	$1$
18513.k1	18513i1	18513.k	18513i	$1$	$1$	$ 3^{2} \cdot 11^{2} \cdot 17 $	$ - 3^{6} \cdot 11^{3} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$0.396891288$	$1$	$4$	$8640$	$0.543286$	$4096000/4913$	$0.90722$	$2.95953$	$[0, 0, 1, 330, -2390]$	$y^2+y=x^3+330x-2390$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(88, 841)]$	$1$
18513.l1	18513g1	18513.l	18513g	$1$	$1$	$ 3^{2} \cdot 11^{2} \cdot 17 $	$ - 3^{6} \cdot 11^{9} \cdot 17^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1$	$1$	$0$	$95040$	$1.742233$	$4096000/4913$	$0.90722$	$4.42371$	$[0, 0, 1, 39930, 3180757]$	$y^2+y=x^3+39930x+3180757$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[ ]$	$1$
32912.b1	32912s1	32912.b	32912s	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 17 $	$ - 2^{12} \cdot 11^{9} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1.360361586$	$1$	$2$	$285120$	$1.886076$	$4096000/4913$	$0.90722$	$4.34496$	$[0, 1, 0, 70987, 7563235]$	$y^2=x^3+x^2+70987x+7563235$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(766, 22627)]$	$1$
32912.d1	32912q1	32912.d	32912q	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 17 $	$ - 2^{12} \cdot 11^{3} \cdot 17^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1$	$1$	$0$	$25920$	$0.687128$	$4096000/4913$	$0.90722$	$2.96177$	$[0, 1, 0, 587, -5469]$	$y^2=x^3+x^2+587x-5469$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[ ]$	$1$
34969.g1	34969c1	34969.g	34969c	$1$	$1$	$ 11^{2} \cdot 17^{2} $	$ - 11^{9} \cdot 17^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$3.596142102$	$1$	$2$	$1140480$	$2.609535$	$4096000/4913$	$0.90722$	$5.14958$	$[0, 1, 1, 1282197, -578352615]$	$y^2+y=x^3+x^2+1282197x-578352615$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(403, 1996)]$	$1$
34969.h1	34969b1	34969.h	34969b	$1$	$1$	$ 11^{2} \cdot 17^{2} $	$ - 11^{3} \cdot 17^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1.113085534$	$1$	$2$	$103680$	$1.410587$	$4096000/4913$	$0.90722$	$3.77440$	$[0, 1, 1, 10597, 438378]$	$y^2+y=x^3+x^2+10597x+438378$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(368, 7369)]$	$1$
51425.q1	51425a1	51425.q	51425a	$1$	$1$	$ 5^{2} \cdot 11^{2} \cdot 17 $	$ - 5^{6} \cdot 11^{9} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$4.359233154$	$1$	$2$	$570240$	$1.997646$	$4096000/4913$	$0.90722$	$4.28963$	$[0, 1, 1, 110917, -14688756]$	$y^2+y=x^3+x^2+110917x-14688756$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(118, 237)]$	$1$
51425.r1	51425c1	51425.r	51425c	$1$	$1$	$ 5^{2} \cdot 11^{2} \cdot 17 $	$ - 5^{6} \cdot 11^{3} \cdot 17^{3} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$0.711002427$	$1$	$12$	$51840$	$0.798699$	$4096000/4913$	$0.90722$	$2.96334$	$[0, 1, 1, 917, 11369]$	$y^2+y=x^3+x^2+917x+11369$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(23, 212), (73, 687)]$	$1$
100793.f1	100793g1	100793.f	100793g	$1$	$1$	$ 7^{2} \cdot 11^{2} \cdot 17 $	$ - 7^{6} \cdot 11^{3} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$0.866327885$	$1$	$4$	$118800$	$0.966935$	$4096000/4913$	$0.90722$	$2.96548$	$[0, 1, 1, 1797, -29760]$	$y^2+y=x^3+x^2+1797x-29760$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(18, 93)]$	$1$
100793.h1	100793d1	100793.h	100793d	$1$	$1$	$ 7^{2} \cdot 11^{2} \cdot 17 $	$ - 7^{6} \cdot 11^{9} \cdot 17^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1$	$1$	$0$	$1306800$	$2.165882$	$4096000/4913$	$0.90722$	$4.21430$	$[0, 1, 1, 217397, 40479863]$	$y^2+y=x^3+x^2+217397x+40479863$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[ ]$	$1$
131648.h1	131648bp1	131648.h	131648bp	$1$	$1$	$ 2^{6} \cdot 11^{2} \cdot 17 $	$ - 2^{6} \cdot 11^{3} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1.462222308$	$1$	$2$	$51840$	$0.340554$	$4096000/4913$	$0.90722$	$2.26065$	$[0, 1, 0, 147, 757]$	$y^2=x^3+x^2+147x+757$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(-4, 11)]$	$1$
131648.n1	131648br1	131648.n	131648br	$1$	$1$	$ 2^{6} \cdot 11^{2} \cdot 17 $	$ - 2^{6} \cdot 11^{9} \cdot 17^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1$	$1$	$0$	$570240$	$1.539501$	$4096000/4913$	$0.90722$	$3.48117$	$[0, 1, 0, 17747, -936531]$	$y^2=x^3+x^2+17747x-936531$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[ ]$	$1$
131648.cf1	131648bg1	131648.cf	131648bg	$1$	$1$	$ 2^{6} \cdot 11^{2} \cdot 17 $	$ - 2^{6} \cdot 11^{9} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$4.733888991$	$1$	$0$	$570240$	$1.539501$	$4096000/4913$	$0.90722$	$3.48117$	$[0, -1, 0, 17747, 936531]$	$y^2=x^3-x^2+17747x+936531$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(19750/9, 3235661/9)]$	$1$
131648.cl1	131648bi1	131648.cl	131648bi	$1$	$1$	$ 2^{6} \cdot 11^{2} \cdot 17 $	$ - 2^{6} \cdot 11^{3} \cdot 17^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1$	$1$	$0$	$51840$	$0.340554$	$4096000/4913$	$0.90722$	$2.26065$	$[0, -1, 0, 147, -757]$	$y^2=x^3-x^2+147x-757$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[ ]$	$1$
296208.cr1	296208cr1	296208.cr	296208cr	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{6} \cdot 11^{9} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$7.370710489$	$1$	$0$	$6842880$	$2.435383$	$4096000/4913$	$0.90722$	$4.11040$	$[0, 0, 0, 638880, -203568464]$	$y^2=x^3+638880x-203568464$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(144353/8, 57726801/8)]$	$1$
296208.dq1	296208dq1	296208.dq	296208dq	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{6} \cdot 11^{3} \cdot 17^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1$	$1$	$0$	$622080$	$1.236433$	$4096000/4913$	$0.90722$	$2.96844$	$[0, 0, 0, 5280, 152944]$	$y^2=x^3+5280x+152944$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[ ]$	$1$
314721.bj1	314721bj1	314721.bj	314721bj	$1$	$1$	$ 3^{2} \cdot 11^{2} \cdot 17^{2} $	$ - 3^{6} \cdot 11^{9} \cdot 17^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1$	$1$	$0$	$27371520$	$3.158840$	$4096000/4913$	$0.90722$	$4.77649$	$[0, 0, 1, 11539770, 15627060369]$	$y^2+y=x^3+11539770x+15627060369$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[ ]$	$1$
314721.bo1	314721bo1	314721.bo	314721bo	$1$	$1$	$ 3^{2} \cdot 11^{2} \cdot 17^{2} $	$ - 3^{6} \cdot 11^{3} \cdot 17^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1$	$1$	$0$	$2488320$	$1.959894$	$4096000/4913$	$0.90722$	$3.64000$	$[0, 0, 1, 95370, -11740842]$	$y^2+y=x^3+95370x-11740842$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[ ]$	$1$
347633.o1	347633o1	347633.o	347633o	$1$	$1$	$ 11^{2} \cdot 13^{2} \cdot 17 $	$ - 11^{9} \cdot 13^{6} \cdot 17^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1$	$1$	$0$	$7603200$	$2.475403$	$4096000/4913$	$0.90722$	$4.09647$	$[0, -1, 1, 749797, -259069328]$	$y^2+y=x^3-x^2+749797x-259069328$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[ ]$	$1$
347633.p1	347633p1	347633.p	347633p	$1$	$1$	$ 11^{2} \cdot 13^{2} \cdot 17 $	$ - 11^{3} \cdot 13^{6} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$6.326859107$	$1$	$0$	$691200$	$1.276455$	$4096000/4913$	$0.90722$	$2.96883$	$[0, -1, 1, 6197, 192389]$	$y^2+y=x^3-x^2+6197x+192389$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(20047/9, 2989837/9)]$	$1$
462825.cj1	462825cj1	462825.cj	462825cj	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 11^{2} \cdot 17 $	$ - 3^{6} \cdot 5^{6} \cdot 11^{9} \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$2.181379716$	$1$	$0$	$13685760$	$2.546951$	$4096000/4913$	$0.90722$	$4.07241$	$[0, 0, 1, 998250, 397594656]$	$y^2+y=x^3+998250x+397594656$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(-2420/3, 282824/3)]$	$1$
462825.cv1	462825cv1	462825.cv	462825cv	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 11^{2} \cdot 17 $	$ - 3^{6} \cdot 5^{6} \cdot 11^{3} \cdot 17^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1$	$1$	$0$	$1244160$	$1.348005$	$4096000/4913$	$0.90722$	$2.96952$	$[0, 0, 1, 8250, -298719]$	$y^2+y=x^3+8250x-298719$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[ ]$	$1$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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