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 (21 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
2652.c1	2652b2	2652.c	2652b	$2$	$2$	$ 2^{2} \cdot 3 \cdot 13 \cdot 17 $	$ 2^{8} \cdot 3^{3} \cdot 13^{2} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$0.976019257$	$1$		$5$	$1728$	$0.548694$	$6371214852688/77571$	$0.95945$	$4.44345$	$[0, -1, 0, -2452, 47560]$	$y^2=x^3-x^2-2452x+47560$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(30, 10)]$
7956.a1	7956b2	7956.a	7956b	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 13 \cdot 17 $	$ 2^{8} \cdot 3^{9} \cdot 13^{2} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$3.766895693$	$1$		$3$	$13824$	$1.098000$	$6371214852688/77571$	$0.95945$	$4.63384$	$[0, 0, 0, -22071, -1262050]$	$y^2=x^3-22071x-1262050$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(382, 6786)]$
10608.z1	10608w2	10608.z	10608w	$2$	$2$	$ 2^{4} \cdot 3 \cdot 13 \cdot 17 $	$ 2^{8} \cdot 3^{3} \cdot 13^{2} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$1$	$4$	$2$	$1$	$6912$	$0.548694$	$6371214852688/77571$	$0.95945$	$3.77890$	$[0, 1, 0, -2452, -47560]$	$y^2=x^3+x^2-2452x-47560$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[]$
31824.l1	31824x2	31824.l	31824x	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 13 \cdot 17 $	$ 2^{8} \cdot 3^{9} \cdot 13^{2} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$4.869925943$	$1$		$1$	$55296$	$1.098000$	$6371214852688/77571$	$0.95945$	$4.01425$	$[0, 0, 0, -22071, 1262050]$	$y^2=x^3-22071x+1262050$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(982/3, 10556/3)]$
34476.c1	34476f2	34476.c	34476f	$2$	$2$	$ 2^{2} \cdot 3 \cdot 13^{2} \cdot 17 $	$ 2^{8} \cdot 3^{3} \cdot 13^{8} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$7.837766372$	$1$		$1$	$290304$	$1.831169$	$6371214852688/77571$	$0.95945$	$4.82557$	$[0, -1, 0, -414444, 102831624]$	$y^2=x^3-x^2-414444x+102831624$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(6809/4, 117131/4)]$
42432.f1	42432ca2	42432.f	42432ca	$2$	$2$	$ 2^{6} \cdot 3 \cdot 13 \cdot 17 $	$ 2^{14} \cdot 3^{3} \cdot 13^{2} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$1$	$4$	$2$	$1$	$55296$	$0.895267$	$6371214852688/77571$	$0.95945$	$3.67756$	$[0, -1, 0, -9809, -370671]$	$y^2=x^3-x^2-9809x-370671$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[]$
42432.bk1	42432bg2	42432.bk	42432bg	$2$	$2$	$ 2^{6} \cdot 3 \cdot 13 \cdot 17 $	$ 2^{14} \cdot 3^{3} \cdot 13^{2} \cdot 17 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$1.058687113$	$1$		$19$	$55296$	$0.895267$	$6371214852688/77571$	$0.95945$	$3.67756$	$[0, 1, 0, -9809, 370671]$	$y^2=x^3+x^2-9809x+370671$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(55, 24), (-41, 840)]$
45084.k1	45084k2	45084.k	45084k	$2$	$2$	$ 2^{2} \cdot 3 \cdot 13 \cdot 17^{2} $	$ 2^{8} \cdot 3^{3} \cdot 13^{2} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$1.706062193$	$1$		$5$	$497664$	$1.965302$	$6371214852688/77571$	$0.95945$	$4.85497$	$[0, 1, 0, -708724, 229410116]$	$y^2=x^3+x^2-708724x+229410116$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(500, 546)]$
66300.bp1	66300bb2	66300.bp	66300bb	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 $	$ 2^{8} \cdot 3^{3} \cdot 5^{6} \cdot 13^{2} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$1$	$1$		$1$	$221184$	$1.353413$	$6371214852688/77571$	$0.95945$	$4.02494$	$[0, 1, 0, -61308, 5822388]$	$y^2=x^3+x^2-61308x+5822388$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[]$
103428.bb1	103428j2	103428.bb	103428j	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 13^{2} \cdot 17 $	$ 2^{8} \cdot 3^{9} \cdot 13^{8} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$7.912778811$	$1$		$1$	$2322432$	$2.380474$	$6371214852688/77571$	$0.95945$	$4.93732$	$[0, 0, 0, -3729999, -2772723850]$	$y^2=x^3-3729999x-2772723850$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(-54493/7, 4250/7)]$
127296.ct1	127296bc2	127296.ct	127296bc	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 13 \cdot 17 $	$ 2^{14} \cdot 3^{9} \cdot 13^{2} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$6.764339819$	$1$		$1$	$442368$	$1.444574$	$6371214852688/77571$	$0.95945$	$3.89463$	$[0, 0, 0, -88284, -10096400]$	$y^2=x^3-88284x-10096400$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(1913/2, 60435/2)]$
127296.dl1	127296db2	127296.dl	127296db	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 13 \cdot 17 $	$ 2^{14} \cdot 3^{9} \cdot 13^{2} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$1$	$1$		$1$	$442368$	$1.444574$	$6371214852688/77571$	$0.95945$	$3.89463$	$[0, 0, 0, -88284, 10096400]$	$y^2=x^3-88284x+10096400$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[]$
129948.ba1	129948bg2	129948.ba	129948bg	$2$	$2$	$ 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \cdot 17 $	$ 2^{8} \cdot 3^{3} \cdot 7^{6} \cdot 13^{2} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$1.570947661$	$1$		$7$	$497664$	$1.521648$	$6371214852688/77571$	$0.95945$	$3.96636$	$[0, 1, 0, -120164, -16072764]$	$y^2=x^3+x^2-120164x-16072764$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(-200, 6)]$
135252.t1	135252o2	135252.t	135252o	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 13 \cdot 17^{2} $	$ 2^{8} \cdot 3^{9} \cdot 13^{2} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$27.54638703$	$1$		$1$	$3981312$	$2.514606$	$6371214852688/77571$	$0.95945$	$4.96144$	$[0, 0, 0, -6378519, -6200451650]$	$y^2=x^3-6378519x-6200451650$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(-21857022390391/122470, 456258526828198227/122470)]$
137904.bx1	137904e2	137904.bx	137904e	$2$	$2$	$ 2^{4} \cdot 3 \cdot 13^{2} \cdot 17 $	$ 2^{8} \cdot 3^{3} \cdot 13^{8} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$1$	$4$	$2$	$1$	$1161216$	$1.831169$	$6371214852688/77571$	$0.95945$	$4.26030$	$[0, 1, 0, -414444, -102831624]$	$y^2=x^3+x^2-414444x-102831624$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[]$
180336.h1	180336ba2	180336.h	180336ba	$2$	$2$	$ 2^{4} \cdot 3 \cdot 13 \cdot 17^{2} $	$ 2^{8} \cdot 3^{3} \cdot 13^{2} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$1$	$4$	$2$	$1$	$1990656$	$1.965302$	$6371214852688/77571$	$0.95945$	$4.29886$	$[0, -1, 0, -708724, -229410116]$	$y^2=x^3-x^2-708724x-229410116$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[]$
198900.cm1	198900cb2	198900.cm	198900cb	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 13 \cdot 17 $	$ 2^{8} \cdot 3^{9} \cdot 5^{6} \cdot 13^{2} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$4.277332555$	$1$		$3$	$1769472$	$1.902719$	$6371214852688/77571$	$0.95945$	$4.20278$	$[0, 0, 0, -551775, -157756250]$	$y^2=x^3-551775x-157756250$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(870, 4550)]$
265200.e1	265200e2	265200.e	265200e	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 $	$ 2^{8} \cdot 3^{3} \cdot 5^{6} \cdot 13^{2} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$4.277915613$	$1$		$3$	$884736$	$1.353413$	$6371214852688/77571$	$0.95945$	$3.57814$	$[0, -1, 0, -61308, -5822388]$	$y^2=x^3-x^2-61308x-5822388$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(1157, 38350)]$
320892.h1	320892h2	320892.h	320892h	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11^{2} \cdot 13 \cdot 17 $	$ 2^{8} \cdot 3^{3} \cdot 11^{6} \cdot 13^{2} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$1$	$16$	$2$	$1$	$2419200$	$1.747643$	$6371214852688/77571$	$0.95945$	$3.89746$	$[0, -1, 0, -296732, -62115480]$	$y^2=x^3-x^2-296732x-62115480$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[]$
389844.cv1	389844cv2	389844.cv	389844cv	$2$	$2$	$ 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 13 \cdot 17 $	$ 2^{8} \cdot 3^{9} \cdot 7^{6} \cdot 13^{2} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$1$	$1$		$1$	$3981312$	$2.070957$	$6371214852688/77571$	$0.95945$	$4.13991$	$[0, 0, 0, -1081479, 432883150]$	$y^2=x^3-1081479x+432883150$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[]$
413712.du1	413712du2	413712.du	413712du	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 13^{2} \cdot 17 $	$ 2^{8} \cdot 3^{9} \cdot 13^{8} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2652$	$12$	$0$	$9.393909606$	$1$		$3$	$9289728$	$2.380474$	$6371214852688/77571$	$0.95945$	$4.40808$	$[0, 0, 0, -3729999, 2772723850]$	$y^2=x^3-3729999x+2772723850$	2.3.0.a.1, 52.6.0.c.1, 204.6.0.?, 2652.12.0.?	$[(563550, 423054320)]$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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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