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
19992.e1	19992i2	19992.e	19992i	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{11} \cdot 3^{3} \cdot 7^{3} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$6.440206044$	$1$		$1$	$27648$	$0.905157$	$81344187038/7803$	$1.04440$	$3.89619$	$[0, -1, 0, -8024, -273972]$	$y^2=x^3-x^2-8024x-273972$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[(421/2, 1525/2)]$
19992.y1	19992o2	19992.y	19992o	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{11} \cdot 3^{3} \cdot 7^{9} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$5.030062879$	$1$		$1$	$193536$	$1.878111$	$81344187038/7803$	$1.04440$	$5.07516$	$[0, 1, 0, -393192, 94758768]$	$y^2=x^3+x^2-393192x+94758768$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[(1461/2, 615/2)]$
39984.bm1	39984d2	39984.bm	39984d	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{11} \cdot 3^{3} \cdot 7^{9} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$1$	$4$	$2$	$1$	$387072$	$1.878111$	$81344187038/7803$	$1.04440$	$4.74317$	$[0, -1, 0, -393192, -94758768]$	$y^2=x^3-x^2-393192x-94758768$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[]$
39984.cj1	39984y2	39984.cj	39984y	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{11} \cdot 3^{3} \cdot 7^{3} \cdot 17^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$0.611319245$	$1$		$23$	$55296$	$0.905157$	$81344187038/7803$	$1.04440$	$3.64132$	$[0, 1, 0, -8024, 273972]$	$y^2=x^3+x^2-8024x+273972$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[(58, 84), (-102, 204)]$
59976.l1	59976bo2	59976.l	59976bo	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{11} \cdot 3^{9} \cdot 7^{9} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$24.13724563$	$1$		$1$	$1548288$	$2.427418$	$81344187038/7803$	$1.04440$	$5.16751$	$[0, 0, 0, -3538731, -2562025466]$	$y^2=x^3-3538731x-2562025466$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[(91116926321/194, 27504164734138863/194)]$
59976.bi1	59976bh2	59976.bi	59976bh	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{11} \cdot 3^{9} \cdot 7^{3} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$1$	$1$		$1$	$221184$	$1.454462$	$81344187038/7803$	$1.04440$	$4.10627$	$[0, 0, 0, -72219, 7469462]$	$y^2=x^3-72219x+7469462$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[]$
119952.bu1	119952bl2	119952.bu	119952bl	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{11} \cdot 3^{9} \cdot 7^{9} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$1$	$1$		$1$	$3096576$	$2.427418$	$81344187038/7803$	$1.04440$	$4.86124$	$[0, 0, 0, -3538731, 2562025466]$	$y^2=x^3-3538731x+2562025466$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[]$
119952.fo1	119952w2	119952.fo	119952w	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{11} \cdot 3^{9} \cdot 7^{3} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$5.705061932$	$1$		$3$	$442368$	$1.454462$	$81344187038/7803$	$1.04440$	$3.86290$	$[0, 0, 0, -72219, -7469462]$	$y^2=x^3-72219x-7469462$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[(746, 18810)]$
159936.bi1	159936iq2	159936.bi	159936iq	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{17} \cdot 3^{3} \cdot 7^{9} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$1$	$1$		$1$	$3096576$	$2.224686$	$81344187038/7803$	$1.04440$	$4.54150$	$[0, -1, 0, -1572769, 759642913]$	$y^2=x^3-x^2-1572769x+759642913$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[]$
159936.ec1	159936em2	159936.ec	159936em	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{17} \cdot 3^{3} \cdot 7^{3} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$1$	$1$		$1$	$442368$	$1.251730$	$81344187038/7803$	$1.04440$	$3.56713$	$[0, -1, 0, -32097, 2223873]$	$y^2=x^3-x^2-32097x+2223873$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[]$
159936.gn1	159936n2	159936.gn	159936n	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{17} \cdot 3^{3} \cdot 7^{9} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$1$	$1$		$1$	$3096576$	$2.224686$	$81344187038/7803$	$1.04440$	$4.54150$	$[0, 1, 0, -1572769, -759642913]$	$y^2=x^3+x^2-1572769x-759642913$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[]$
159936.jq1	159936hh2	159936.jq	159936hh	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ 2^{17} \cdot 3^{3} \cdot 7^{3} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$1$	$1$		$1$	$442368$	$1.251730$	$81344187038/7803$	$1.04440$	$3.56713$	$[0, 1, 0, -32097, -2223873]$	$y^2=x^3+x^2-32097x-2223873$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[]$
339864.l1	339864l2	339864.l	339864l	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 17^{2} $	$ 2^{11} \cdot 3^{3} \cdot 7^{9} \cdot 17^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$1$	$4$	$2$	$1$	$55738368$	$3.294720$	$81344187038/7803$	$1.04440$	$5.28089$	$[0, -1, 0, -113632584, 466231622508]$	$y^2=x^3-x^2-113632584x+466231622508$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[]$
339864.cs1	339864cs2	339864.cs	339864cs	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 17^{2} $	$ 2^{11} \cdot 3^{3} \cdot 7^{3} \cdot 17^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$17.31022126$	$1$		$1$	$7962624$	$2.321762$	$81344187038/7803$	$1.04440$	$4.36419$	$[0, 1, 0, -2319032, -1359938448]$	$y^2=x^3+x^2-2319032x-1359938448$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[(62605573/82, 488291638575/82)]$
479808.ef1	479808ef2	479808.ef	479808ef	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{17} \cdot 3^{9} \cdot 7^{3} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$3.105483020$	$1$		$5$	$3538944$	$1.801037$	$81344187038/7803$	$1.04440$	$3.77145$	$[0, 0, 0, -288876, 59755696]$	$y^2=x^3-288876x+59755696$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[(344, 1044)]$
479808.ei1	479808ei2	479808.ei	479808ei	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{17} \cdot 3^{9} \cdot 7^{3} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$1$	$1$		$1$	$3538944$	$1.801037$	$81344187038/7803$	$1.04440$	$3.77145$	$[0, 0, 0, -288876, -59755696]$	$y^2=x^3-288876x-59755696$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[]$
479808.nx1	479808nx2	479808.nx	479808nx	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{17} \cdot 3^{9} \cdot 7^{9} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$9.264260307$	$1$		$1$	$24772608$	$2.773991$	$81344187038/7803$	$1.04440$	$4.66399$	$[0, 0, 0, -14154924, 20496203728]$	$y^2=x^3-14154924x+20496203728$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[(90764/5, 16278912/5)]$
479808.oa1	479808oa2	479808.oa	479808oa	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ 2^{17} \cdot 3^{9} \cdot 7^{9} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$1$	$1$		$1$	$24772608$	$2.773991$	$81344187038/7803$	$1.04440$	$4.66399$	$[0, 0, 0, -14154924, -20496203728]$	$y^2=x^3-14154924x-20496203728$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[]$
499800.ch1	499800ch2	499800.ch	499800ch	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 $	$ 2^{11} \cdot 3^{3} \cdot 5^{6} \cdot 7^{9} \cdot 17^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$29.36292530$	$1$		$3$	$24772608$	$2.682831$	$81344187038/7803$	$1.04440$	$4.56611$	$[0, -1, 0, -9829808, 11864505612]$	$y^2=x^3-x^2-9829808x+11864505612$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[(1897, 6350), (16573/3, 55700/3)]$
499800.hp1	499800hp2	499800.hp	499800hp	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 $	$ 2^{11} \cdot 3^{3} \cdot 5^{6} \cdot 7^{3} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2856$	$12$	$0$	$1$	$4$	$2$	$1$	$3538944$	$1.709875$	$81344187038/7803$	$1.04440$	$3.67635$	$[0, 1, 0, -200608, -34647712]$	$y^2=x^3+x^2-200608x-34647712$	2.3.0.a.1, 168.6.0.?, 408.6.0.?, 476.6.0.?, 2856.12.0.?	$[]$

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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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