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 (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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
3757.a2	3757d1	3757.a	3757d	$2$	$2$	$ 13 \cdot 17^{2} $	$ 13^{2} \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$0.394422319$	$1$		$9$	$512$	$-0.069784$	$9129329/169$	$0.83854$	$2.97965$	$[1, 0, 0, -74, 235]$	$y^2+xy=x^3-74x+235$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[(3, 5)]$
3757.c2	3757c1	3757.c	3757c	$2$	$2$	$ 13 \cdot 17^{2} $	$ 13^{2} \cdot 17^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$5.095374233$	$1$		$1$	$8704$	$1.346823$	$9129329/169$	$0.83854$	$5.04483$	$[1, 1, 1, -21392, 1175944]$	$y^2+xy+y=x^3+x^2-21392x+1175944$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[(676/3, -943/3)]$
33813.h2	33813g1	33813.h	33813g	$2$	$2$	$ 3^{2} \cdot 13 \cdot 17^{2} $	$ 3^{6} \cdot 13^{2} \cdot 17^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$1$	$208896$	$1.896128$	$9129329/169$	$0.83854$	$4.61400$	$[1, -1, 0, -192528, -31943021]$	$y^2+xy=x^3-x^2-192528x-31943021$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[]$
33813.m2	33813f1	33813.m	33813f	$2$	$2$	$ 3^{2} \cdot 13 \cdot 17^{2} $	$ 3^{6} \cdot 13^{2} \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$1$	$12288$	$0.479522$	$9129329/169$	$0.83854$	$2.98394$	$[1, -1, 0, -666, -6345]$	$y^2+xy=x^3-x^2-666x-6345$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[]$
48841.b2	48841d1	48841.b	48841d	$2$	$2$	$ 13^{2} \cdot 17^{2} $	$ 13^{8} \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$3.505284927$	$1$		$3$	$86016$	$1.212690$	$9129329/169$	$0.83854$	$3.69722$	$[1, 0, 1, -12510, 528803]$	$y^2+xy+y=x^3-12510x+528803$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[(143, 1220)]$
48841.e2	48841c1	48841.e	48841c	$2$	$2$	$ 13^{2} \cdot 17^{2} $	$ 13^{8} \cdot 17^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$22.36799669$	$1$		$1$	$1462272$	$2.629295$	$9129329/169$	$0.83854$	$5.27176$	$[1, 1, 0, -3615251, 2601625616]$	$y^2+xy=x^3+x^2-3615251x+2601625616$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[(-116903799491/9468, 61168814723740447/9468)]$
60112.f2	60112v1	60112.f	60112v	$2$	$2$	$ 2^{4} \cdot 13 \cdot 17^{2} $	$ 2^{12} \cdot 13^{2} \cdot 17^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$1$	$557056$	$2.039970$	$9129329/169$	$0.83854$	$4.52961$	$[0, 1, 0, -342272, -75944972]$	$y^2=x^3+x^2-342272x-75944972$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[]$
60112.u2	60112r1	60112.u	60112r	$2$	$2$	$ 2^{4} \cdot 13 \cdot 17^{2} $	$ 2^{12} \cdot 13^{2} \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$1$	$32768$	$0.623363$	$9129329/169$	$0.83854$	$2.98478$	$[0, -1, 0, -1184, -15040]$	$y^2=x^3-x^2-1184x-15040$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[]$
93925.r2	93925h1	93925.r	93925h	$2$	$2$	$ 5^{2} \cdot 13 \cdot 17^{2} $	$ 5^{6} \cdot 13^{2} \cdot 17^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$1$	$1114112$	$2.151543$	$9129329/169$	$0.83854$	$4.46999$	$[1, 0, 1, -534801, 148062623]$	$y^2+xy+y=x^3-534801x+148062623$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[]$
93925.u2	93925g1	93925.u	93925g	$2$	$2$	$ 5^{2} \cdot 13 \cdot 17^{2} $	$ 5^{6} \cdot 13^{2} \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$1$	$65536$	$0.734935$	$9129329/169$	$0.83854$	$2.98537$	$[1, 1, 0, -1850, 29375]$	$y^2+xy=x^3+x^2-1850x+29375$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[]$
184093.f2	184093f1	184093.f	184093f	$2$	$2$	$ 7^{2} \cdot 13 \cdot 17^{2} $	$ 7^{6} \cdot 13^{2} \cdot 17^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$6.233335194$	$1$		$1$	$3342336$	$2.319778$	$9129329/169$	$0.83854$	$4.38840$	$[1, 0, 0, -1048209, -406493480]$	$y^2+xy=x^3-1048209x-406493480$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[(-2157/2, 13519/2)]$
184093.i2	184093i1	184093.i	184093i	$2$	$2$	$ 7^{2} \cdot 13 \cdot 17^{2} $	$ 7^{6} \cdot 13^{2} \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$7.290715308$	$1$		$1$	$196608$	$0.903171$	$9129329/169$	$0.83854$	$2.98618$	$[1, 1, 1, -3627, -84232]$	$y^2+xy+y=x^3+x^2-3627x-84232$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[(-6249/14, 85973/14)]$
240448.c2	240448c1	240448.c	240448c	$2$	$2$	$ 2^{6} \cdot 13 \cdot 17^{2} $	$ 2^{18} \cdot 13^{2} \cdot 17^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$1$	$4456448$	$2.386543$	$9129329/169$	$0.83854$	$4.35847$	$[0, 1, 0, -1369089, 606190687]$	$y^2=x^3+x^2-1369089x+606190687$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[]$
240448.m2	240448m1	240448.m	240448m	$2$	$2$	$ 2^{6} \cdot 13 \cdot 17^{2} $	$ 2^{18} \cdot 13^{2} \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$2.153430833$	$1$		$3$	$262144$	$0.969936$	$9129329/169$	$0.83854$	$2.98648$	$[0, 1, 0, -4737, -125057]$	$y^2=x^3+x^2-4737x-125057$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[(-38, 39)]$
240448.bv2	240448bv1	240448.bv	240448bv	$2$	$2$	$ 2^{6} \cdot 13 \cdot 17^{2} $	$ 2^{18} \cdot 13^{2} \cdot 17^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$15.19908207$	$1$		$1$	$4456448$	$2.386543$	$9129329/169$	$0.83854$	$4.35847$	$[0, -1, 0, -1369089, -606190687]$	$y^2=x^3-x^2-1369089x-606190687$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[(-19700776/163, 3743640849/163)]$
240448.cd2	240448cd1	240448.cd	240448cd	$2$	$2$	$ 2^{6} \cdot 13 \cdot 17^{2} $	$ 2^{18} \cdot 13^{2} \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$1$	$262144$	$0.969936$	$9129329/169$	$0.83854$	$2.98648$	$[0, -1, 0, -4737, 125057]$	$y^2=x^3-x^2-4737x+125057$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[]$
439569.o2	439569o1	439569.o	439569o	$2$	$2$	$ 3^{2} \cdot 13^{2} \cdot 17^{2} $	$ 3^{6} \cdot 13^{8} \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$1$	$2064384$	$1.761997$	$9129329/169$	$0.83854$	$3.57932$	$[1, -1, 1, -112586, -14277688]$	$y^2+xy+y=x^3-x^2-112586x-14277688$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[]$
439569.ba2	439569ba1	439569.ba	439569ba	$2$	$2$	$ 3^{2} \cdot 13^{2} \cdot 17^{2} $	$ 3^{6} \cdot 13^{8} \cdot 17^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$9$	$3$	$1$	$35094528$	$3.178604$	$9129329/169$	$0.83854$	$4.88760$	$[1, -1, 1, -32537264, -70276428894]$	$y^2+xy+y=x^3-x^2-32537264x-70276428894$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[]$
454597.n2	454597n1	454597.n	454597n	$2$	$2$	$ 11^{2} \cdot 13 \cdot 17^{2} $	$ 11^{6} \cdot 13^{2} \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$3.853129928$	$1$		$1$	$737280$	$1.129164$	$9129329/169$	$0.83854$	$2.98714$	$[1, 0, 1, -8957, -321741]$	$y^2+xy+y=x^3-8957x-321741$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[(-201/2, 561/2)]$
454597.y2	454597y1	454597.y	454597y	$2$	$2$	$ 11^{2} \cdot 13 \cdot 17^{2} $	$ 11^{6} \cdot 13^{2} \cdot 17^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$884$	$12$	$0$	$80.70031511$	$1$		$1$	$12533760$	$2.545769$	$9129329/169$	$0.83854$	$4.29205$	$[1, 1, 0, -2588434, -1578123873]$	$y^2+xy=x^3+x^2-2588434x-1578123873$	2.3.0.a.1, 34.6.0.a.1, 52.6.0.d.1, 884.12.0.?	$[(-465357973946108720438330439453297189/23648558097722926, -3287790452500037792886615324941556803118882587605041/23648558097722926)]$

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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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