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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
5720.e1	5720a2	5720.e	5720a	$2$	$2$	$ 2^{3} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{11} \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$1$	$2304$	$0.366591$	$8331019058/39325$	$0.82593$	$3.52160$	$[0, -1, 0, -536, 4940]$	$y^2=x^3-x^2-536x+4940$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[ ]$
11440.e1	11440b2	11440.e	11440b	$2$	$2$	$ 2^{4} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{11} \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$0.803176957$	$1$		$7$	$4608$	$0.366591$	$8331019058/39325$	$0.82593$	$3.26038$	$[0, 1, 0, -536, -4940]$	$y^2=x^3+x^2-536x-4940$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[(-14, 4)]$
28600.f1	28600r2	28600.f	28600r	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 11 \cdot 13 $	$ 2^{11} \cdot 5^{8} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$1$	$55296$	$1.171310$	$8331019058/39325$	$0.82593$	$3.91033$	$[0, 1, 0, -13408, 590688]$	$y^2=x^3+x^2-13408x+590688$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[ ]$
45760.h1	45760t2	45760.h	45760t	$2$	$2$	$ 2^{6} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{17} \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$0.537558827$	$1$		$9$	$36864$	$0.713164$	$8331019058/39325$	$0.82593$	$3.22675$	$[0, 1, 0, -2145, 37375]$	$y^2=x^3+x^2-2145x+37375$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[(35, 80)]$
45760.bx1	45760bz2	45760.bx	45760bz	$2$	$2$	$ 2^{6} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{17} \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$3.889265193$	$1$		$1$	$36864$	$0.713164$	$8331019058/39325$	$0.82593$	$3.22675$	$[0, -1, 0, -2145, -37375]$	$y^2=x^3-x^2-2145x-37375$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[(853/3, 20944/3)]$
51480.y1	51480br2	51480.y	51480br	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{11} \cdot 3^{6} \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$1$	$55296$	$0.915897$	$8331019058/39325$	$0.82593$	$3.41596$	$[0, 0, 0, -4827, -128554]$	$y^2=x^3-4827x-128554$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[ ]$
57200.bw1	57200f2	57200.bw	57200f	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 11 \cdot 13 $	$ 2^{11} \cdot 5^{8} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$1$	$110592$	$1.171310$	$8331019058/39325$	$0.82593$	$3.66290$	$[0, -1, 0, -13408, -590688]$	$y^2=x^3-x^2-13408x-590688$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[ ]$
62920.t1	62920u2	62920.t	62920u	$2$	$2$	$ 2^{3} \cdot 5 \cdot 11^{2} \cdot 13 $	$ 2^{11} \cdot 5^{2} \cdot 11^{8} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$9$	$3$	$1$	$276480$	$1.565538$	$8331019058/39325$	$0.82593$	$4.05944$	$[0, -1, 0, -64896, -6315604]$	$y^2=x^3-x^2-64896x-6315604$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[ ]$
74360.u1	74360r2	74360.u	74360r	$2$	$2$	$ 2^{3} \cdot 5 \cdot 11 \cdot 13^{2} $	$ 2^{11} \cdot 5^{2} \cdot 11^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$5.633234441$	$1$		$1$	$387072$	$1.649065$	$8331019058/39325$	$0.82593$	$4.08834$	$[0, -1, 0, -90640, 10490700]$	$y^2=x^3-x^2-90640x+10490700$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[(17445/7, 1652820/7)]$
102960.et1	102960bq2	102960.et	102960bq	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{11} \cdot 3^{6} \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$1$	$110592$	$0.915897$	$8331019058/39325$	$0.82593$	$3.21082$	$[0, 0, 0, -4827, 128554]$	$y^2=x^3-4827x+128554$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[ ]$
125840.k1	125840p2	125840.k	125840p	$2$	$2$	$ 2^{4} \cdot 5 \cdot 11^{2} \cdot 13 $	$ 2^{11} \cdot 5^{2} \cdot 11^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1.108232936$	$1$		$7$	$552960$	$1.565538$	$8331019058/39325$	$0.82593$	$3.81982$	$[0, 1, 0, -64896, 6315604]$	$y^2=x^3+x^2-64896x+6315604$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[(84, 1210)]$
148720.l1	148720bf2	148720.l	148720bf	$2$	$2$	$ 2^{4} \cdot 5 \cdot 11 \cdot 13^{2} $	$ 2^{11} \cdot 5^{2} \cdot 11^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1.682827078$	$1$		$3$	$774144$	$1.649065$	$8331019058/39325$	$0.82593$	$3.85040$	$[0, 1, 0, -90640, -10490700]$	$y^2=x^3+x^2-90640x-10490700$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[(420, 5070)]$
228800.h1	228800h2	228800.h	228800h	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 11 \cdot 13 $	$ 2^{17} \cdot 5^{8} \cdot 11^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$2.901312734$	$1$		$3$	$884736$	$1.517883$	$8331019058/39325$	$0.82593$	$3.58843$	$[0, 1, 0, -53633, -4779137]$	$y^2=x^3+x^2-53633x-4779137$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[(273, 1000)]$
228800.gd1	228800gh2	228800.gd	228800gh	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 11 \cdot 13 $	$ 2^{17} \cdot 5^{8} \cdot 11^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$5.576115534$	$1$		$1$	$884736$	$1.517883$	$8331019058/39325$	$0.82593$	$3.58843$	$[0, -1, 0, -53633, 4779137]$	$y^2=x^3-x^2-53633x+4779137$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[(6043/3, 444500/3)]$
257400.eg1	257400eg2	257400.eg	257400eg	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13 $	$ 2^{11} \cdot 3^{6} \cdot 5^{8} \cdot 11^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$9.654159815$	$1$		$1$	$1327104$	$1.720615$	$8331019058/39325$	$0.82593$	$3.74978$	$[0, 0, 0, -120675, -16069250]$	$y^2=x^3-120675x-16069250$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[(134985/14, 41385875/14)]$
280280.i1	280280i2	280280.i	280280i	$2$	$2$	$ 2^{3} \cdot 5 \cdot 7^{2} \cdot 11 \cdot 13 $	$ 2^{11} \cdot 5^{2} \cdot 7^{6} \cdot 11^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$8.613477657$	$1$		$1$	$663552$	$1.339546$	$8331019058/39325$	$0.82593$	$3.35976$	$[0, 1, 0, -26280, -1641872]$	$y^2=x^3+x^2-26280x-1641872$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[(36191/5, 6842164/5)]$
314600.h1	314600h2	314600.h	314600h	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$ 2^{11} \cdot 5^{8} \cdot 11^{8} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$1$	$6635520$	$2.370258$	$8331019058/39325$	$0.82593$	$4.30616$	$[0, 1, 0, -1622408, -792695312]$	$y^2=x^3+x^2-1622408x-792695312$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[ ]$
371800.c1	371800c2	371800.c	371800c	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 11 \cdot 13^{2} $	$ 2^{11} \cdot 5^{8} \cdot 11^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$3.836944635$	$1$		$3$	$9289728$	$2.453785$	$8331019058/39325$	$0.82593$	$4.32822$	$[0, 1, 0, -2266008, 1306805488]$	$y^2=x^3+x^2-2266008x+1306805488$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[(603, 12650)]$
411840.bc1	411840bc2	411840.bc	411840bc	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{17} \cdot 3^{6} \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$1$	$884736$	$1.262470$	$8331019058/39325$	$0.82593$	$3.18821$	$[0, 0, 0, -19308, -1028432]$	$y^2=x^3-19308x-1028432$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[ ]$
411840.gc1	411840gc2	411840.gc	411840gc	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{17} \cdot 3^{6} \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$1$	$884736$	$1.262470$	$8331019058/39325$	$0.82593$	$3.18821$	$[0, 0, 0, -19308, 1028432]$	$y^2=x^3-19308x+1028432$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[ ]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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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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