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

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Results (22 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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
20280.d2	20280f2	20280.d	20280f	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{8} \cdot 3^{7} \cdot 5^{12} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$4$	$2$	$1$	$225792$	$2.036030$	$116227003261808/533935546875$	$1.04468$	$4.79598$	$[0, -1, 0, 83924, 24621076]$	$y^2=x^3-x^2+83924x+24621076$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[]$
20280.q2	20280v2	20280.q	20280v	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{8} \cdot 3^{7} \cdot 5^{12} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$2935296$	$3.318504$	$116227003261808/533935546875$	$1.04468$	$6.34777$	$[0, -1, 0, 14183100, 54149236452]$	$y^2=x^3-x^2+14183100x+54149236452$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[]$
40560.cb2	40560v2	40560.cb	40560v	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{8} \cdot 3^{7} \cdot 5^{12} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$3.037814162$	$1$		$3$	$451584$	$2.036030$	$116227003261808/533935546875$	$1.04468$	$4.48268$	$[0, 1, 0, 83924, -24621076]$	$y^2=x^3+x^2+83924x-24621076$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[(251, 3510)]$
40560.ck2	40560be2	40560.ck	40560be	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{8} \cdot 3^{7} \cdot 5^{12} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$5870592$	$3.318504$	$116227003261808/533935546875$	$1.04468$	$5.93310$	$[0, 1, 0, 14183100, -54149236452]$	$y^2=x^3+x^2+14183100x-54149236452$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[]$
60840.t2	60840s2	60840.t	60840s	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{8} \cdot 3^{13} \cdot 5^{12} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$32.81275367$	$1$		$1$	$23482368$	$3.867809$	$116227003261808/533935546875$	$1.04468$	$6.31309$	$[0, 0, 0, 127647897, -1462157032102]$	$y^2=x^3+127647897x-1462157032102$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[(6683006708813474/456403, 567697033876746724303678/456403)]$
60840.bh2	60840cc2	60840.bh	60840cc	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{8} \cdot 3^{13} \cdot 5^{12} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.684689412$	$1$		$9$	$1806336$	$2.585335$	$116227003261808/533935546875$	$1.04468$	$4.91606$	$[0, 0, 0, 755313, -665524366]$	$y^2=x^3+755313x-665524366$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[(673, 12150)]$
101400.ce2	101400bq2	101400.ce	101400bq	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{8} \cdot 3^{7} \cdot 5^{18} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$8.698583787$	$1$		$3$	$70447104$	$4.123222$	$116227003261808/533935546875$	$1.04468$	$6.29921$	$[0, 1, 0, 354577492, 6769363711488]$	$y^2=x^3+x^2+354577492x+6769363711488$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[(63772, 16992288)]$
101400.dk2	101400dn2	101400.dk	101400dn	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{8} \cdot 3^{7} \cdot 5^{18} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$5419008$	$2.840748$	$116227003261808/533935546875$	$1.04468$	$4.96409$	$[0, 1, 0, 2098092, 3081830688]$	$y^2=x^3+x^2+2098092x+3081830688$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[]$
121680.p2	121680bc2	121680.p	121680bc	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{8} \cdot 3^{13} \cdot 5^{12} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$33.76750657$	$1$		$1$	$46964736$	$3.867809$	$116227003261808/533935546875$	$1.04468$	$5.93937$	$[0, 0, 0, 127647897, 1462157032102]$	$y^2=x^3+127647897x+1462157032102$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[(27719049219234854/1706171, 9346117376578791575597922/1706171)]$
121680.ff2	121680bz2	121680.ff	121680bz	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{8} \cdot 3^{13} \cdot 5^{12} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$3612672$	$2.585335$	$116227003261808/533935546875$	$1.04468$	$4.62504$	$[0, 0, 0, 755313, 665524366]$	$y^2=x^3+755313x+665524366$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[]$
162240.i2	162240dk2	162240.i	162240dk	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{14} \cdot 3^{7} \cdot 5^{12} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$21.22767407$	$1$		$1$	$46964736$	$3.665077$	$116227003261808/533935546875$	$1.04468$	$5.59416$	$[0, -1, 0, 56732399, -433250624015]$	$y^2=x^3-x^2+56732399x-433250624015$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[(146671437459/1343, 56389355942762596/1343)]$
162240.dt2	162240da2	162240.dt	162240da	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{14} \cdot 3^{7} \cdot 5^{12} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$3612672$	$2.382603$	$116227003261808/533935546875$	$1.04468$	$4.31135$	$[0, -1, 0, 335695, -197304303]$	$y^2=x^3-x^2+335695x-197304303$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[]$
162240.fx2	162240gn2	162240.fx	162240gn	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{14} \cdot 3^{7} \cdot 5^{12} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$8.663431457$	$1$		$3$	$46964736$	$3.665077$	$116227003261808/533935546875$	$1.04468$	$5.59416$	$[0, 1, 0, 56732399, 433250624015]$	$y^2=x^3+x^2+56732399x+433250624015$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[(6266, 1017249)]$
162240.gr2	162240es2	162240.gr	162240es	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{14} \cdot 3^{7} \cdot 5^{12} \cdot 13^{3} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.575642368$	$1$		$33$	$3612672$	$2.382603$	$116227003261808/533935546875$	$1.04468$	$4.31135$	$[0, 1, 0, 335695, 197304303]$	$y^2=x^3+x^2+335695x+197304303$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[(901, 35100), (-149, 12000)]$
202800.bh2	202800ji2	202800.bh	202800ji	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{8} \cdot 3^{7} \cdot 5^{18} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$10838016$	$2.840748$	$116227003261808/533935546875$	$1.04468$	$4.68252$	$[0, -1, 0, 2098092, -3081830688]$	$y^2=x^3-x^2+2098092x-3081830688$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[]$
202800.ep2	202800kg2	202800.ep	202800kg	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{8} \cdot 3^{7} \cdot 5^{18} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$49$	$7$	$1$	$140894208$	$4.123222$	$116227003261808/533935546875$	$1.04468$	$5.94191$	$[0, -1, 0, 354577492, -6769363711488]$	$y^2=x^3-x^2+354577492x-6769363711488$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[]$
304200.bw2	304200bw2	304200.bw	304200bw	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{8} \cdot 3^{13} \cdot 5^{18} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$9$	$3$	$1$	$563576832$	$4.672531$	$116227003261808/533935546875$	$1.04468$	$6.27318$	$[0, 0, 0, 3191197425, -182769629012750]$	$y^2=x^3+3191197425x-182769629012750$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[]$
304200.ea2	304200ea2	304200.ea	304200ea	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{8} \cdot 3^{13} \cdot 5^{18} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$22.94155325$	$1$		$1$	$43352064$	$3.390057$	$116227003261808/533935546875$	$1.04468$	$5.05424$	$[0, 0, 0, 18882825, -83190545750]$	$y^2=x^3+18882825x-83190545750$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[(52617335039/965, 12102476118677712/965)]$
486720.ct2	486720ct2	486720.ct	486720ct	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{14} \cdot 3^{13} \cdot 5^{12} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$13.93666963$	$1$		$1$	$28901376$	$2.931911$	$116227003261808/533935546875$	$1.04468$	$4.45301$	$[0, 0, 0, 3021252, -5324194928]$	$y^2=x^3+3021252x-5324194928$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[(3058253/17, 5408028261/17)]$
486720.fw2	486720fw2	486720.fw	486720fw	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{14} \cdot 3^{13} \cdot 5^{12} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$28901376$	$2.931911$	$116227003261808/533935546875$	$1.04468$	$4.45301$	$[0, 0, 0, 3021252, 5324194928]$	$y^2=x^3+3021252x+5324194928$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[]$
486720.kz2	486720kz2	486720.kz	486720kz	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{14} \cdot 3^{13} \cdot 5^{12} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$4.260991581$	$1$		$3$	$375717888$	$4.214386$	$116227003261808/533935546875$	$1.04468$	$5.62821$	$[0, 0, 0, 510591588, 11697256256816]$	$y^2=x^3+510591588x+11697256256816$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[(201202, 90882000)]$
486720.oj2	486720oj2	486720.oj	486720oj	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{14} \cdot 3^{13} \cdot 5^{12} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$4$	$2$	$1$	$375717888$	$4.214386$	$116227003261808/533935546875$	$1.04468$	$5.62821$	$[0, 0, 0, 510591588, -11697256256816]$	$y^2=x^3+510591588x-11697256256816$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?	$[]$

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Classical	Maass
Hilbert	Bianchi

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

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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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