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 (34 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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
3360.h1	3360q3	3360.h	3360q	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7 $	$ 2^{9} \cdot 3^{7} \cdot 5^{4} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$1$	$4$	$2$	$1$	$215040$	$2.759987$	$229625675762164624948320008/9568125$	$[0, -1, 0, -102060000, 396888659352]$	$y^2=x^3-x^2-102060000x+396888659352$
3360.x1	3360x2	3360.x	3360x	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7 $	$ 2^{9} \cdot 3^{7} \cdot 5^{4} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$1$	$4$	$2$	$1$	$215040$	$2.759987$	$229625675762164624948320008/9568125$	$[0, 1, 0, -102060000, -396888659352]$	$y^2=x^3+x^2-102060000x-396888659352$
6720.c1	6720bi3	6720.c	6720bi	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 $	$ 2^{15} \cdot 3^{7} \cdot 5^{4} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$1$	$36$	$2, 3$	$1$	$860160$	$3.106560$	$229625675762164624948320008/9568125$	$[0, -1, 0, -408240001, -3174701034815]$	$y^2=x^3-x^2-408240001x-3174701034815$
6720.bx1	6720cb3	6720.bx	6720cb	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 $	$ 2^{15} \cdot 3^{7} \cdot 5^{4} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$1$	$1$		$1$	$860160$	$3.106560$	$229625675762164624948320008/9568125$	$[0, 1, 0, -408240001, 3174701034815]$	$y^2=x^3+x^2-408240001x+3174701034815$
10080.b1	10080n3	10080.b	10080n	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 7 $	$ 2^{9} \cdot 3^{13} \cdot 5^{4} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$1$	$1$		$1$	$1720320$	$3.309292$	$229625675762164624948320008/9568125$	$[0, 0, 0, -918540003, 10715075262502]$	$y^2=x^3-918540003x+10715075262502$
10080.z1	10080t2	10080.z	10080t	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 7 $	$ 2^{9} \cdot 3^{13} \cdot 5^{4} \cdot 7 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$77.04433215$	$1$		$1$	$1720320$	$3.309292$	$229625675762164624948320008/9568125$	$[0, 0, 0, -918540003, -10715075262502]$	$y^2=x^3-918540003x-10715075262502$
16800.z1	16800i2	16800.z	16800i	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 $	$ 2^{9} \cdot 3^{7} \cdot 5^{10} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$100$	$2, 5$	$1$	$5160960$	$3.564705$	$229625675762164624948320008/9568125$	$[0, -1, 0, -2551500008, -49605979418988]$	$y^2=x^3-x^2-2551500008x-49605979418988$
16800.be1	16800r3	16800.be	16800r	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 $	$ 2^{9} \cdot 3^{7} \cdot 5^{10} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$5160960$	$3.564705$	$229625675762164624948320008/9568125$	$[0, 1, 0, -2551500008, 49605979418988]$	$y^2=x^3+x^2-2551500008x+49605979418988$
20160.ea1	20160et3	20160.ea	20160et	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 $	$ 2^{15} \cdot 3^{13} \cdot 5^{4} \cdot 7 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$1$	$4$	$2$	$3$	$6881280$	$3.655869$	$229625675762164624948320008/9568125$	$[0, 0, 0, -3674160012, 85720602100016]$	$y^2=x^3-3674160012x+85720602100016$
20160.ek1	20160fi3	20160.ek	20160fi	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 $	$ 2^{15} \cdot 3^{13} \cdot 5^{4} \cdot 7 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$18.80924723$	$4$	$2$	$1$	$6881280$	$3.655869$	$229625675762164624948320008/9568125$	$[0, 0, 0, -3674160012, -85720602100016]$	$y^2=x^3-3674160012x-85720602100016$
23520.m1	23520bf4	23520.m	23520bf	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} $	$ 2^{9} \cdot 3^{7} \cdot 5^{4} \cdot 7^{7} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$35.77773686$	$1$		$3$	$10321920$	$3.732944$	$229625675762164624948320008/9568125$	$[0, -1, 0, -5000940016, 136122808277716]$	$y^2=x^3-x^2-5000940016x+136122808277716$
23520.ba1	23520br4	23520.ba	23520br	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} $	$ 2^{9} \cdot 3^{7} \cdot 5^{4} \cdot 7^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$1$	$16$	$2$	$1$	$10321920$	$3.732944$	$229625675762164624948320008/9568125$	$[0, 1, 0, -5000940016, -136122808277716]$	$y^2=x^3+x^2-5000940016x-136122808277716$
33600.ca1	33600eo4	33600.ca	33600eo	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 $	$ 2^{15} \cdot 3^{7} \cdot 5^{10} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$16$	$2$	$1$	$20643840$	$3.911282$	$229625675762164624948320008/9568125$	$[0, -1, 0, -10206000033, 396858041351937]$	$y^2=x^3-x^2-10206000033x+396858041351937$
33600.fi1	33600gy4	33600.fi	33600gy	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 $	$ 2^{15} \cdot 3^{7} \cdot 5^{10} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$20643840$	$3.911282$	$229625675762164624948320008/9568125$	$[0, 1, 0, -10206000033, -396858041351937]$	$y^2=x^3+x^2-10206000033x-396858041351937$
47040.dk1	47040fk4	47040.dk	47040fk	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} $	$ 2^{15} \cdot 3^{7} \cdot 5^{4} \cdot 7^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$1$	$4$	$2$	$1$	$41287680$	$4.079514$	$229625675762164624948320008/9568125$	$[0, -1, 0, -20003760065, -1088962462461663]$	$y^2=x^3-x^2-20003760065x-1088962462461663$
47040.ft1	47040hi4	47040.ft	47040hi	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} $	$ 2^{15} \cdot 3^{7} \cdot 5^{4} \cdot 7^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$1.367256411$	$1$		$7$	$41287680$	$4.079514$	$229625675762164624948320008/9568125$	$[0, 1, 0, -20003760065, 1088962462461663]$	$y^2=x^3+x^2-20003760065x+1088962462461663$
50400.ca1	50400df4	50400.ca	50400df	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7 $	$ 2^{9} \cdot 3^{13} \cdot 5^{10} \cdot 7 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$144.9475263$	$4$	$2$	$1$	$41287680$	$4.114014$	$229625675762164624948320008/9568125$	$[0, 0, 0, -22963500075, -1339384407812750]$	$y^2=x^3-22963500075x-1339384407812750$
50400.cq1	50400dw4	50400.cq	50400dw	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7 $	$ 2^{9} \cdot 3^{13} \cdot 5^{10} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$9$	$3$	$1$	$41287680$	$4.114014$	$229625675762164624948320008/9568125$	$[0, 0, 0, -22963500075, 1339384407812750]$	$y^2=x^3-22963500075x+1339384407812750$
70560.cn1	70560bv4	70560.cn	70560bv	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ 2^{9} \cdot 3^{13} \cdot 5^{4} \cdot 7^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.13	2B	$1$	$9$	$3$	$1$	$82575360$	$4.282249$	$229625675762164624948320008/9568125$	$[0, 0, 0, -45008460147, -3675270815038186]$	$y^2=x^3-45008460147x-3675270815038186$
70560.ed1	70560bs4	70560.ed	70560bs	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ 2^{9} \cdot 3^{13} \cdot 5^{4} \cdot 7^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.13	2B	$1$	$16$	$2$	$1$	$82575360$	$4.282249$	$229625675762164624948320008/9568125$	$[0, 0, 0, -45008460147, 3675270815038186]$	$y^2=x^3-45008460147x+3675270815038186$
100800.r1	100800mi4	100800.r	100800mi	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7 $	$ 2^{15} \cdot 3^{13} \cdot 5^{10} \cdot 7 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$77.74008751$	$1$		$1$	$165150720$	$4.460587$	$229625675762164624948320008/9568125$	$[0, 0, 0, -91854000300, -10715075262502000]$	$y^2=x^3-91854000300x-10715075262502000$
100800.or1	100800nv4	100800.or	100800nv	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7 $	$ 2^{15} \cdot 3^{13} \cdot 5^{10} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$16$	$2$	$1$	$165150720$	$4.460587$	$229625675762164624948320008/9568125$	$[0, 0, 0, -91854000300, 10715075262502000]$	$y^2=x^3-91854000300x+10715075262502000$
117600.k1	117600bc4	117600.k	117600bc	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ 2^{9} \cdot 3^{7} \cdot 5^{10} \cdot 7^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$247726080$	$4.537659$	$229625675762164624948320008/9568125$	$[0, -1, 0, -125023500408, -17015100987713688]$	$y^2=x^3-x^2-125023500408x-17015100987713688$
117600.hq1	117600de4	117600.hq	117600de	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ 2^{9} \cdot 3^{7} \cdot 5^{10} \cdot 7^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$10.93518453$	$1$		$1$	$247726080$	$4.537659$	$229625675762164624948320008/9568125$	$[0, 1, 0, -125023500408, 17015100987713688]$	$y^2=x^3+x^2-125023500408x+17015100987713688$
141120.r1	141120cx3	141120.r	141120cx	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ 2^{15} \cdot 3^{13} \cdot 5^{4} \cdot 7^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.14	2B	$1$	$1$		$1$	$330301440$	$4.628822$	$229625675762164624948320008/9568125$	$[0, 0, 0, -180033840588, 29402166520305488]$	$y^2=x^3-180033840588x+29402166520305488$
141120.gn1	141120ek4	141120.gn	141120ek	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ 2^{15} \cdot 3^{13} \cdot 5^{4} \cdot 7^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.14	2B	$1$	$25$	$5$	$1$	$330301440$	$4.628822$	$229625675762164624948320008/9568125$	$[0, 0, 0, -180033840588, -29402166520305488]$	$y^2=x^3-180033840588x-29402166520305488$
235200.co1	235200co3	235200.co	235200co	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ 2^{15} \cdot 3^{7} \cdot 5^{10} \cdot 7^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$45.80388947$	$1$		$1$	$990904320$	$4.884232$	$229625675762164624948320008/9568125$	$[0, -1, 0, -500094001633, 136121307995711137]$	$y^2=x^3-x^2-500094001633x+136121307995711137$
235200.bbs1	235200bbs4	235200.bbs	235200bbs	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ 2^{15} \cdot 3^{7} \cdot 5^{10} \cdot 7^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$36$	$2, 3$	$1$	$990904320$	$4.884232$	$229625675762164624948320008/9568125$	$[0, 1, 0, -500094001633, -136121307995711137]$	$y^2=x^3+x^2-500094001633x-136121307995711137$
352800.bf1	352800bf4	352800.bf	352800bf	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ 2^{9} \cdot 3^{13} \cdot 5^{10} \cdot 7^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$64$	$2$	$1$	$1981808640$	$5.086967$	$229625675762164624948320008/9568125$	$[0, 0, 0, -1125211503675, -459408851879773250]$	$y^2=x^3-1125211503675x-459408851879773250$
352800.mg1	352800mg2	352800.mg	352800mg	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ 2^{9} \cdot 3^{13} \cdot 5^{10} \cdot 7^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$1981808640$	$5.086967$	$229625675762164624948320008/9568125$	$[0, 0, 0, -1125211503675, 459408851879773250]$	$y^2=x^3-1125211503675x+459408851879773250$
406560.ch1	406560ch4	406560.ch	406560ch	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{9} \cdot 3^{7} \cdot 5^{4} \cdot 7 \cdot 11^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$35.76739467$	$4$	$2$	$1$	$275251200$	$3.958935$	$229625675762164624948320008/9568125$	$[0, -1, 0, -12349260040, -528209408557400]$	$y^2=x^3-x^2-12349260040x-528209408557400$
406560.fv1	406560fv2	406560.fv	406560fv	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{9} \cdot 3^{7} \cdot 5^{4} \cdot 7 \cdot 11^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2.287038645$	$1$		$5$	$275251200$	$3.958935$	$229625675762164624948320008/9568125$	$[0, 1, 0, -12349260040, 528209408557400]$	$y^2=x^3+x^2-12349260040x+528209408557400$
705600.ix1	-	705600.ix	-	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ 2^{15} \cdot 3^{13} \cdot 5^{10} \cdot 7^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$7927234560$	$5.433540$	$229625675762164624948320008/9568125$	$[0, 0, 0, -4500846014700, 3675270815038186000]$	$y^2=x^3-4500846014700x+3675270815038186000$
705600.byh1	-	705600.byh	-	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ 2^{15} \cdot 3^{13} \cdot 5^{10} \cdot 7^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$196$	$2, 7$	$1$	$7927234560$	$5.433540$	$229625675762164624948320008/9568125$	$[0, 0, 0, -4500846014700, -3675270815038186000]$	$y^2=x^3-4500846014700x-3675270815038186000$

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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.