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 (20 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
8190.e2	8190a1	8190.e	8190a	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{2} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$0.445520153$	$1$	$9$	$1280$	$-0.114125$	$108531333/63700$	$0.87684$	$2.41918$	$[1, -1, 0, 30, 0]$	$y^2+xy=x^3-x^2+30x$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(3, 9)]$
8190.bl2	8190be1	8190.bl	8190be	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{2} \cdot 3^{9} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.785304871$	$1$	$3$	$3840$	$0.435182$	$108531333/63700$	$0.87684$	$3.15072$	$[1, -1, 1, 268, -269]$	$y^2+xy+y=x^3-x^2+268x-269$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(41, 259)]$
40950.bt2	40950k1	40950.bt	40950k	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 $	$ - 2^{2} \cdot 3^{9} \cdot 5^{8} \cdot 7^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.183066309$	$1$	$7$	$92160$	$1.239901$	$108531333/63700$	$0.87684$	$3.58251$	$[1, -1, 0, 6708, -26884]$	$y^2+xy=x^3-x^2+6708x-26884$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(29, 423)]$
40950.fl2	40950df1	40950.fl	40950df	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 $	$ - 2^{2} \cdot 3^{3} \cdot 5^{8} \cdot 7^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$30720$	$0.690595$	$108531333/63700$	$0.87684$	$2.96184$	$[1, -1, 1, 745, 747]$	$y^2+xy+y=x^3-x^2+745x+747$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[ ]$
57330.cx2	57330k1	57330.cx	57330k	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 $	$ - 2^{2} \cdot 3^{3} \cdot 5^{2} \cdot 7^{8} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$61440$	$0.858830$	$108531333/63700$	$0.87684$	$3.05514$	$[1, -1, 0, 1461, -2927]$	$y^2+xy=x^3-x^2+1461x-2927$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[ ]$
57330.dg2	57330dd1	57330.dg	57330dd	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 $	$ - 2^{2} \cdot 3^{9} \cdot 5^{2} \cdot 7^{8} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$184320$	$1.408136$	$108531333/63700$	$0.87684$	$3.65675$	$[1, -1, 1, 13147, 65881]$	$y^2+xy+y=x^3-x^2+13147x+65881$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[ ]$
65520.bb2	65520bx1	65520.bb	65520bx	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{14} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$0.777477255$	$1$	$9$	$30720$	$0.579022$	$108531333/63700$	$0.87684$	$2.71559$	$[0, 0, 0, 477, -478]$	$y^2=x^3+477x-478$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(31, 210)]$
65520.ei2	65520ch1	65520.ei	65520ch	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{14} \cdot 3^{9} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$92160$	$1.128328$	$108531333/63700$	$0.87684$	$3.30996$	$[0, 0, 0, 4293, 12906]$	$y^2=x^3+4293x+12906$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[ ]$
106470.bq2	106470i1	106470.bq	106470i	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13^{2} $	$ - 2^{2} \cdot 3^{9} \cdot 5^{2} \cdot 7^{2} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$645120$	$1.717657$	$108531333/63700$	$0.87684$	$3.78207$	$[1, -1, 0, 45345, -454375]$	$y^2+xy=x^3-x^2+45345x-454375$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[ ]$
106470.fm2	106470dv1	106470.fm	106470dv	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13^{2} $	$ - 2^{2} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$215040$	$1.168350$	$108531333/63700$	$0.87684$	$3.21262$	$[1, -1, 1, 5038, 15149]$	$y^2+xy+y=x^3-x^2+5038x+15149$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[ ]$
262080.df2	262080df1	262080.df	262080df	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{20} \cdot 3^{9} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$737280$	$1.474903$	$108531333/63700$	$0.87684$	$3.27552$	$[0, 0, 0, 17172, -103248]$	$y^2=x^3+17172x-103248$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[ ]$
262080.el2	262080el1	262080.el	262080el	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{20} \cdot 3^{9} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$737280$	$1.474903$	$108531333/63700$	$0.87684$	$3.27552$	$[0, 0, 0, 17172, 103248]$	$y^2=x^3+17172x+103248$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[ ]$
262080.ho2	262080ho1	262080.ho	262080ho	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{20} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.412624657$	$1$	$5$	$245760$	$0.925596$	$108531333/63700$	$0.87684$	$2.74719$	$[0, 0, 0, 1908, 3824]$	$y^2=x^3+1908x+3824$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(8, 140)]$
262080.nc2	262080nc1	262080.nc	262080nc	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{20} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.104661097$	$1$	$5$	$245760$	$0.925596$	$108531333/63700$	$0.87684$	$2.74719$	$[0, 0, 0, 1908, -3824]$	$y^2=x^3+1908x-3824$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(32, 300)]$
286650.be2	286650be1	286650.be	286650be	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$ - 2^{2} \cdot 3^{9} \cdot 5^{8} \cdot 7^{8} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$4423680$	$2.212856$	$108531333/63700$	$0.87684$	$3.95687$	$[1, -1, 0, 328683, 8563841]$	$y^2+xy=x^3-x^2+328683x+8563841$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[ ]$
286650.pu2	286650pu1	286650.pu	286650pu	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$ - 2^{2} \cdot 3^{3} \cdot 5^{8} \cdot 7^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$6.453573818$	$1$	$3$	$1474560$	$1.663549$	$108531333/63700$	$0.87684$	$3.43231$	$[1, -1, 1, 36520, -329353]$	$y^2+xy+y=x^3-x^2+36520x-329353$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(7689, 670555)]$
327600.bs2	327600bs1	327600.bs	327600bs	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 $	$ - 2^{14} \cdot 3^{3} \cdot 5^{8} \cdot 7^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.467357477$	$1$	$7$	$737280$	$1.383741$	$108531333/63700$	$0.87684$	$3.13183$	$[0, 0, 0, 11925, -59750]$	$y^2=x^3+11925x-59750$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(15, 350)]$
327600.fx2	327600fx1	327600.fx	327600fx	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 $	$ - 2^{14} \cdot 3^{9} \cdot 5^{8} \cdot 7^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.255609040$	$1$	$5$	$2211840$	$1.933048$	$108531333/63700$	$0.87684$	$3.65087$	$[0, 0, 0, 107325, 1613250]$	$y^2=x^3+107325x+1613250$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(255, 6750)]$
458640.ga2	458640ga1	458640.ga	458640ga	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 $	$ - 2^{14} \cdot 3^{9} \cdot 5^{2} \cdot 7^{8} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$4423680$	$2.101284$	$108531333/63700$	$0.87684$	$3.71151$	$[0, 0, 0, 210357, -4426758]$	$y^2=x^3+210357x-4426758$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[ ]$
458640.ir2	458640ir1	458640.ir	458640ir	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 $	$ - 2^{14} \cdot 3^{3} \cdot 5^{2} \cdot 7^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$3.829144724$	$1$	$3$	$1474560$	$1.551977$	$108531333/63700$	$0.87684$	$3.20586$	$[0, 0, 0, 23373, 163954]$	$y^2=x^3+23373x+163954$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(263, 4950)]$

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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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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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