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 (28 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
4992.a1	4992f2	4992.a	4992f	$2$	$2$	$ 2^{7} \cdot 3 \cdot 13 $	$ 2^{14} \cdot 3^{3} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1.530924441$	$1$	$5$	$1536$	$0.202849$	$8821888/4563$	$1.13046$	$3.01762$	$[0, -1, 0, -109, -107]$	$y^2=x^3-x^2-109x-107$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(-9, 8)]$
4992.d1	4992d1	4992.d	4992d	$2$	$2$	$ 2^{7} \cdot 3 \cdot 13 $	$ 2^{8} \cdot 3^{3} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$768$	$-0.143724$	$8821888/4563$	$1.13046$	$2.52923$	$[0, -1, 0, -27, 27]$	$y^2=x^3-x^2-27x+27$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$
4992.e1	4992b2	4992.e	4992b	$2$	$2$	$ 2^{7} \cdot 3 \cdot 13 $	$ 2^{14} \cdot 3^{3} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$0.874969845$	$1$	$7$	$1536$	$0.202849$	$8821888/4563$	$1.13046$	$3.01762$	$[0, 1, 0, -109, 107]$	$y^2=x^3+x^2-109x+107$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(-7, 24)]$
4992.h1	4992h1	4992.h	4992h	$2$	$2$	$ 2^{7} \cdot 3 \cdot 13 $	$ 2^{8} \cdot 3^{3} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$0.685795568$	$1$	$5$	$768$	$-0.143724$	$8821888/4563$	$1.13046$	$2.52923$	$[0, 1, 0, -27, -27]$	$y^2=x^3+x^2-27x-27$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(-3, 6)]$
14976.c1	14976j1	14976.c	14976j	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 13 $	$ 2^{8} \cdot 3^{9} \cdot 13^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1.036116058$	$1$	$17$	$6144$	$0.405582$	$8821888/4563$	$1.13046$	$2.92584$	$[0, 0, 0, -246, 484]$	$y^2=x^3-246x+484$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(-1, 27), (26, 108)]$
14976.h1	14976h1	14976.h	14976h	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 13 $	$ 2^{8} \cdot 3^{9} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$6144$	$0.405582$	$8821888/4563$	$1.13046$	$2.92584$	$[0, 0, 0, -246, -484]$	$y^2=x^3-246x-484$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$
14976.bd1	14976r2	14976.bd	14976r	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 13 $	$ 2^{14} \cdot 3^{9} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$2.508264443$	$1$	$5$	$12288$	$0.752155$	$8821888/4563$	$1.13046$	$3.35841$	$[0, 0, 0, -984, 3872]$	$y^2=x^3-984x+3872$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(-4, 88)]$
14976.bg1	14976bg2	14976.bg	14976bg	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 13 $	$ 2^{14} \cdot 3^{9} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$12288$	$0.752155$	$8821888/4563$	$1.13046$	$3.35841$	$[0, 0, 0, -984, -3872]$	$y^2=x^3-984x-3872$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$
64896.d1	64896i1	64896.d	64896i	$2$	$2$	$ 2^{7} \cdot 3 \cdot 13^{2} $	$ 2^{8} \cdot 3^{3} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1.464864443$	$1$	$5$	$129024$	$1.138750$	$8821888/4563$	$1.13046$	$3.33265$	$[0, -1, 0, -4619, 40923]$	$y^2=x^3-x^2-4619x+40923$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(-17, 338)]$
64896.q1	64896h2	64896.q	64896h	$2$	$2$	$ 2^{7} \cdot 3 \cdot 13^{2} $	$ 2^{14} \cdot 3^{3} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$8.765145480$	$1$	$1$	$258048$	$1.485325$	$8821888/4563$	$1.13046$	$3.70799$	$[0, -1, 0, -18477, -308907]$	$y^2=x^3-x^2-18477x-308907$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(64364/17, 12596077/17)]$
64896.x1	64896s1	64896.x	64896s	$2$	$2$	$ 2^{7} \cdot 3 \cdot 13^{2} $	$ 2^{8} \cdot 3^{3} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$129024$	$1.138750$	$8821888/4563$	$1.13046$	$3.33265$	$[0, 1, 0, -4619, -40923]$	$y^2=x^3+x^2-4619x-40923$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$
64896.bk1	64896bk2	64896.bk	64896bk	$2$	$2$	$ 2^{7} \cdot 3 \cdot 13^{2} $	$ 2^{14} \cdot 3^{3} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$2.627926983$	$1$	$3$	$258048$	$1.485325$	$8821888/4563$	$1.13046$	$3.70799$	$[0, 1, 0, -18477, 308907]$	$y^2=x^3+x^2-18477x+308907$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(134, 507)]$
124800.f1	124800dj2	124800.f	124800dj	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{14} \cdot 3^{3} \cdot 5^{6} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$196608$	$1.007568$	$8821888/4563$	$1.13046$	$3.01279$	$[0, -1, 0, -2733, 18837]$	$y^2=x^3-x^2-2733x+18837$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$
124800.cp1	124800w1	124800.cp	124800w	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{8} \cdot 3^{3} \cdot 5^{6} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$98304$	$0.660995$	$8821888/4563$	$1.13046$	$2.65837$	$[0, -1, 0, -683, -2013]$	$y^2=x^3-x^2-683x-2013$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$
124800.dd1	124800cn1	124800.dd	124800cn	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{8} \cdot 3^{3} \cdot 5^{6} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1.275068256$	$1$	$5$	$98304$	$0.660995$	$8821888/4563$	$1.13046$	$2.65837$	$[0, 1, 0, -683, 2013]$	$y^2=x^3+x^2-683x+2013$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(28, 75)]$
124800.fn1	124800bx2	124800.fn	124800bx	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{14} \cdot 3^{3} \cdot 5^{6} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$196608$	$1.007568$	$8821888/4563$	$1.13046$	$3.01279$	$[0, 1, 0, -2733, -18837]$	$y^2=x^3+x^2-2733x-18837$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$
194688.o1	194688ch2	194688.o	194688ch	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 13^{2} $	$ 2^{14} \cdot 3^{9} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$2064384$	$2.034630$	$8821888/4563$	$1.13046$	$3.91474$	$[0, 0, 0, -166296, -8506784]$	$y^2=x^3-166296x-8506784$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$
194688.v1	194688h2	194688.v	194688h	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 13^{2} $	$ 2^{14} \cdot 3^{9} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$6.771351438$	$1$	$3$	$2064384$	$2.034630$	$8821888/4563$	$1.13046$	$3.91474$	$[0, 0, 0, -166296, 8506784]$	$y^2=x^3-166296x+8506784$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(33865, 6231537)]$
194688.cu1	194688bd1	194688.cu	194688bd	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{9} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$4.704892873$	$1$	$1$	$1032192$	$1.688057$	$8821888/4563$	$1.13046$	$3.57326$	$[0, 0, 0, -41574, -1063348]$	$y^2=x^3-41574x-1063348$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(-884/3, 38870/3)]$
194688.df1	194688bj1	194688.df	194688bj	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 13^{2} $	$ 2^{8} \cdot 3^{9} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$3.679946761$	$1$	$3$	$1032192$	$1.688057$	$8821888/4563$	$1.13046$	$3.57326$	$[0, 0, 0, -41574, 1063348]$	$y^2=x^3-41574x+1063348$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(-121, 2079)]$
244608.v1	244608v1	244608.v	244608v	$2$	$2$	$ 2^{7} \cdot 3 \cdot 7^{2} \cdot 13 $	$ 2^{8} \cdot 3^{3} \cdot 7^{6} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$221184$	$0.829231$	$8821888/4563$	$1.13046$	$2.67690$	$[0, -1, 0, -1339, 6595]$	$y^2=x^3-x^2-1339x+6595$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$
244608.cj1	244608cj2	244608.cj	244608cj	$2$	$2$	$ 2^{7} \cdot 3 \cdot 7^{2} \cdot 13 $	$ 2^{14} \cdot 3^{3} \cdot 7^{6} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$442368$	$1.175804$	$8821888/4563$	$1.13046$	$3.01209$	$[0, -1, 0, -5357, -47403]$	$y^2=x^3-x^2-5357x-47403$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$
244608.dv1	244608dv1	244608.dv	244608dv	$2$	$2$	$ 2^{7} \cdot 3 \cdot 7^{2} \cdot 13 $	$ 2^{8} \cdot 3^{3} \cdot 7^{6} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1.446942850$	$1$	$5$	$221184$	$0.829231$	$8821888/4563$	$1.13046$	$2.67690$	$[0, 1, 0, -1339, -6595]$	$y^2=x^3+x^2-1339x-6595$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(-31, 78)]$
244608.fj1	244608fj2	244608.fj	244608fj	$2$	$2$	$ 2^{7} \cdot 3 \cdot 7^{2} \cdot 13 $	$ 2^{14} \cdot 3^{3} \cdot 7^{6} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$442368$	$1.175804$	$8821888/4563$	$1.13046$	$3.01209$	$[0, 1, 0, -5357, 47403]$	$y^2=x^3+x^2-5357x+47403$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$
374400.z1	374400z2	374400.z	374400z	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{14} \cdot 3^{9} \cdot 5^{6} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$1572864$	$1.556875$	$8821888/4563$	$1.13046$	$3.26851$	$[0, 0, 0, -24600, -484000]$	$y^2=x^3-24600x-484000$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$
374400.bh1	374400bh1	374400.bh	374400bh	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{8} \cdot 3^{9} \cdot 5^{6} \cdot 13^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$3.058366885$	$1$	$15$	$786432$	$1.210300$	$8821888/4563$	$1.13046$	$2.94444$	$[0, 0, 0, -6150, -60500]$	$y^2=x^3-6150x-60500$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(-49, 351), (86, 216)]$
374400.kh1	374400kh2	374400.kh	374400kh	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{14} \cdot 3^{9} \cdot 5^{6} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$3.244951165$	$1$	$3$	$1572864$	$1.556875$	$8821888/4563$	$1.13046$	$3.26851$	$[0, 0, 0, -24600, 484000]$	$y^2=x^3-24600x+484000$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[(41/2, 3861/2)]$
374400.kl1	374400kl1	374400.kl	374400kl	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{8} \cdot 3^{9} \cdot 5^{6} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$312$	$12$	$0$	$1$	$1$	$1$	$786432$	$1.210300$	$8821888/4563$	$1.13046$	$2.94444$	$[0, 0, 0, -6150, 60500]$	$y^2=x^3-6150x+60500$	2.3.0.a.1, 12.6.0.a.1, 104.6.0.?, 312.12.0.?	$[ ]$

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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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