LMFDB - Elliptic curve search results

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Conductor	j-invariant	Rank	Torsion	Complex multiplication

Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image

Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $\|Ш\|	Nonmax$\ \ell$

Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (25 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	Semistable	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
1045.b3	1045b1	1045.b	1045b	$4$	$4$	$ 5 \cdot 11 \cdot 19 $	$ 5^{4} \cdot 11 \cdot 19^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.6	2B	$6.655271875$	$1$		$1$	$4416$	$1.715824$	$104857852278310619039721/47155625$	$[1, -1, 0, -982409, -374543312]$	$y^2+xy=x^3-x^2-982409x-374543312$
5225.a3	5225b1	5225.a	5225b	$4$	$4$	$ 5^{2} \cdot 11 \cdot 19 $	$ 5^{10} \cdot 11 \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$105984$	$2.520542$	$104857852278310619039721/47155625$	$[1, -1, 1, -24560230, -46842474228]$	$y^2+xy+y=x^3-x^2-24560230x-46842474228$
9405.d3	9405i1	9405.d	9405i	$4$	$4$	$ 3^{2} \cdot 5 \cdot 11 \cdot 19 $	$ 3^{6} \cdot 5^{4} \cdot 11 \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$1$	$1$		$1$	$141312$	$2.265129$	$104857852278310619039721/47155625$	$[1, -1, 1, -8841683, 10121511106]$	$y^2+xy+y=x^3-x^2-8841683x+10121511106$
11495.b3	11495f1	11495.b	11495f	$4$	$4$	$ 5 \cdot 11^{2} \cdot 19 $	$ 5^{4} \cdot 11^{7} \cdot 19^{3} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.7	2B	$10.86473607$	$1$		$3$	$529920$	$2.914772$	$104857852278310619039721/47155625$	$[1, -1, 1, -118871512, 498873762786]$	$y^2+xy+y=x^3-x^2-118871512x+498873762786$
16720.u3	16720bh1	16720.u	16720bh	$4$	$4$	$ 2^{4} \cdot 5 \cdot 11 \cdot 19 $	$ 2^{12} \cdot 5^{4} \cdot 11 \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.6	2B	$1$	$1$		$1$	$282624$	$2.408970$	$104857852278310619039721/47155625$	$[0, 0, 0, -15718547, 23986490514]$	$y^2=x^3-15718547x+23986490514$
19855.a3	19855c1	19855.a	19855c	$4$	$4$	$ 5 \cdot 11 \cdot 19^{2} $	$ 5^{4} \cdot 11 \cdot 19^{9} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.7	2B	$13.23829366$	$1$		$3$	$1589760$	$3.188042$	$104857852278310619039721/47155625$	$[1, -1, 1, -354649717, 2570765825484]$	$y^2+xy+y=x^3-x^2-354649717x+2570765825484$
47025.bh3	47025be1	47025.bh	47025be	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 11 \cdot 19 $	$ 3^{6} \cdot 5^{10} \cdot 11 \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$1$	$1$		$1$	$3391488$	$3.069851$	$104857852278310619039721/47155625$	$[1, -1, 0, -221042067, 1264967846216]$	$y^2+xy=x^3-x^2-221042067x+1264967846216$
51205.p3	51205d1	51205.p	51205d	$4$	$4$	$ 5 \cdot 7^{2} \cdot 11 \cdot 19 $	$ 5^{4} \cdot 7^{6} \cdot 11 \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$1$	$1$		$1$	$1695744$	$2.688778$	$104857852278310619039721/47155625$	$[1, -1, 0, -48138050, 128564632111]$	$y^2+xy=x^3-x^2-48138050x+128564632111$
57475.k3	57475i1	57475.k	57475i	$4$	$4$	$ 5^{2} \cdot 11^{2} \cdot 19 $	$ 5^{10} \cdot 11^{7} \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$12718080$	$3.719490$	$104857852278310619039721/47155625$	$[1, -1, 0, -2971787792, 62356248560491]$	$y^2+xy=x^3-x^2-2971787792x+62356248560491$
66880.bn3	66880ce1	66880.bn	66880ce	$4$	$4$	$ 2^{6} \cdot 5 \cdot 11 \cdot 19 $	$ 2^{18} \cdot 5^{4} \cdot 11 \cdot 19^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.12	2B	$2.454927175$	$1$		$3$	$2260992$	$2.755547$	$104857852278310619039721/47155625$	$[0, 0, 0, -62874188, 191891924112]$	$y^2=x^3-62874188x+191891924112$
66880.bq3	66880m1	66880.bq	66880m	$4$	$4$	$ 2^{6} \cdot 5 \cdot 11 \cdot 19 $	$ 2^{18} \cdot 5^{4} \cdot 11 \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.12	2B	$1$	$1$		$1$	$2260992$	$2.755547$	$104857852278310619039721/47155625$	$[0, 0, 0, -62874188, -191891924112]$	$y^2=x^3-62874188x-191891924112$
83600.bk3	83600bq1	83600.bk	83600bq	$4$	$4$	$ 2^{4} \cdot 5^{2} \cdot 11 \cdot 19 $	$ 2^{12} \cdot 5^{10} \cdot 11 \cdot 19^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$7.199881817$	$1$		$1$	$6782976$	$3.213692$	$104857852278310619039721/47155625$	$[0, 0, 0, -392963675, 2998311314250]$	$y^2=x^3-392963675x+2998311314250$
99275.e3	99275a1	99275.e	99275a	$4$	$4$	$ 5^{2} \cdot 11 \cdot 19^{2} $	$ 5^{10} \cdot 11 \cdot 19^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$1$	$9$	$3$	$1$	$38154240$	$3.992764$	$104857852278310619039721/47155625$	$[1, -1, 0, -8866242917, 321336861942616]$	$y^2+xy=x^3-x^2-8866242917x+321336861942616$
103455.v3	103455m1	103455.v	103455m	$4$	$4$	$ 3^{2} \cdot 5 \cdot 11^{2} \cdot 19 $	$ 3^{6} \cdot 5^{4} \cdot 11^{7} \cdot 19^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$106.0064475$	$1$		$1$	$16957440$	$3.464077$	$104857852278310619039721/47155625$	$[1, -1, 0, -1069843605, -13468521751624]$	$y^2+xy=x^3-x^2-1069843605x-13468521751624$
150480.y3	150480bt1	150480.y	150480bt	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 19 $	$ 2^{12} \cdot 3^{6} \cdot 5^{4} \cdot 11 \cdot 19^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$38.05887800$	$1$		$1$	$9043968$	$2.958279$	$104857852278310619039721/47155625$	$[0, 0, 0, -141466923, -647635243878]$	$y^2=x^3-141466923x-647635243878$
176605.d3	176605g1	176605.d	176605g	$4$	$4$	$ 5 \cdot 11 \cdot 13^{2} \cdot 19 $	$ 5^{4} \cdot 11 \cdot 13^{6} \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$1$	$1$		$1$	$10174464$	$2.998299$	$104857852278310619039721/47155625$	$[1, -1, 1, -166027153, -823369737888]$	$y^2+xy+y=x^3-x^2-166027153x-823369737888$
178695.u3	178695x1	178695.u	178695x	$4$	$4$	$ 3^{2} \cdot 5 \cdot 11 \cdot 19^{2} $	$ 3^{6} \cdot 5^{4} \cdot 11 \cdot 19^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$1$	$25$	$5$	$1$	$50872320$	$3.737350$	$104857852278310619039721/47155625$	$[1, -1, 0, -3191847450, -69407485440625]$	$y^2+xy=x^3-x^2-3191847450x-69407485440625$
183920.bq3	183920q1	183920.bq	183920q	$4$	$4$	$ 2^{4} \cdot 5 \cdot 11^{2} \cdot 19 $	$ 2^{12} \cdot 5^{4} \cdot 11^{7} \cdot 19^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.8	2B	$15.05050555$	$1$		$1$	$33914880$	$3.607918$	$104857852278310619039721/47155625$	$[0, 0, 0, -1901944187, -31926018874134]$	$y^2=x^3-1901944187x-31926018874134$
218405.j3	218405i1	218405.j	218405i	$4$	$4$	$ 5 \cdot 11^{2} \cdot 19^{2} $	$ 5^{4} \cdot 11^{7} \cdot 19^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.14	2B	$1$	$4$	$2$	$1$	$190771200$	$4.386993$	$104857852278310619039721/47155625$	$[1, -1, 0, -42912615719, -3421560575872400]$	$y^2+xy=x^3-x^2-42912615719x-3421560575872400$
256025.c3	256025c1	256025.c	256025c	$4$	$4$	$ 5^{2} \cdot 7^{2} \cdot 11 \cdot 19 $	$ 5^{10} \cdot 7^{6} \cdot 11 \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$1$	$1$		$1$	$40697856$	$3.493500$	$104857852278310619039721/47155625$	$[1, -1, 1, -1203451255, 16069375562622]$	$y^2+xy+y=x^3-x^2-1203451255x+16069375562622$
302005.j3	302005j1	302005.j	302005j	$4$	$4$	$ 5 \cdot 11 \cdot 17^{2} \cdot 19 $	$ 5^{4} \cdot 11 \cdot 17^{6} \cdot 19^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$76.28759141$	$1$		$1$	$20348928$	$3.132431$	$104857852278310619039721/47155625$	$[1, -1, 0, -283916255, -1841266956800]$	$y^2+xy=x^3-x^2-283916255x-1841266956800$
317680.bo3	317680bo1	317680.bo	317680bo	$4$	$4$	$ 2^{4} \cdot 5 \cdot 11 \cdot 19^{2} $	$ 2^{12} \cdot 5^{4} \cdot 11 \cdot 19^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.12.0.8	2B	$57.14289463$	$1$		$1$	$101744640$	$3.881191$	$104857852278310619039721/47155625$	$[0, 0, 0, -5674395467, -164523338435526]$	$y^2=x^3-5674395467x-164523338435526$
334400.dm3	334400dm1	334400.dm	334400dm	$4$	$4$	$ 2^{6} \cdot 5^{2} \cdot 11 \cdot 19 $	$ 2^{18} \cdot 5^{10} \cdot 11 \cdot 19^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$4.033699427$	$1$		$1$	$54263808$	$3.560265$	$104857852278310619039721/47155625$	$[0, 0, 0, -1571854700, 23986490514000]$	$y^2=x^3-1571854700x+23986490514000$
334400.ds3	334400ds1	334400.ds	334400ds	$4$	$4$	$ 2^{6} \cdot 5^{2} \cdot 11 \cdot 19 $	$ 2^{18} \cdot 5^{10} \cdot 11 \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$1$	$25$	$5$	$1$	$54263808$	$3.560265$	$104857852278310619039721/47155625$	$[0, 0, 0, -1571854700, -23986490514000]$	$y^2=x^3-1571854700x-23986490514000$
460845.bc3	460845bc1	460845.bc	460845bc	$4$	$4$	$ 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \cdot 19 $	$ 3^{6} \cdot 5^{4} \cdot 7^{6} \cdot 11 \cdot 19^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	4.6.0.1	2B	$8.789535056$	$4$	$2$	$3$	$54263808$	$3.238087$	$104857852278310619039721/47155625$	$[1, -1, 1, -433242452, -3470811824546]$	$y^2+xy+y=x^3-x^2-433242452x-3470811824546$

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Elliptic 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.