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 (32 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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
5760.d1	5760d2	5760.d	5760d	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 $	$ 2^{13} \cdot 3^{9} \cdot 5^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$0.992481996$	$1$	$9$	$3072$	$0.802242$	$1149984/625$	$1.24048$	$3.79430$	$[0, 0, 0, -1188, -3888]$	$y^2=x^3-1188x-3888$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-18, 108)]$
5760.e2	5760c1	5760.e	5760c	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 $	$ 2^{7} \cdot 3^{3} \cdot 5^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1.537996740$	$1$	$3$	$512$	$-0.093637$	$1149984/625$	$1.24048$	$2.55271$	$[0, 0, 0, -33, 18]$	$y^2=x^3-33x+18$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(6, 6)]$
5760.t1	5760b2	5760.t	5760b	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 $	$ 2^{13} \cdot 3^{9} \cdot 5^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$2.103724111$	$1$	$5$	$3072$	$0.802242$	$1149984/625$	$1.24048$	$3.79430$	$[0, 0, 0, -1188, 3888]$	$y^2=x^3-1188x+3888$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(72, 540)]$
5760.u2	5760bd1	5760.u	5760bd	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 $	$ 2^{7} \cdot 3^{3} \cdot 5^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1$	$1$	$1$	$512$	$-0.093637$	$1149984/625$	$1.24048$	$2.55271$	$[0, 0, 0, -33, -18]$	$y^2=x^3-33x-18$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[ ]$
5760.bd1	5760bh2	5760.bd	5760bh	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 $	$ 2^{13} \cdot 3^{3} \cdot 5^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$0.308331628$	$1$	$11$	$1024$	$0.252936$	$1149984/625$	$1.24048$	$3.03302$	$[0, 0, 0, -132, 144]$	$y^2=x^3-132x+144$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-2, 20)]$
5760.be2	5760bg1	5760.be	5760bg	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 $	$ 2^{7} \cdot 3^{9} \cdot 5^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1.634015511$	$1$	$3$	$1536$	$0.455669$	$1149984/625$	$1.24048$	$3.31399$	$[0, 0, 0, -297, -486]$	$y^2=x^3-297x-486$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-2, 10)]$
5760.bp1	5760bf2	5760.bp	5760bf	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 $	$ 2^{13} \cdot 3^{3} \cdot 5^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$0.735160958$	$1$	$7$	$1024$	$0.252936$	$1149984/625$	$1.24048$	$3.03302$	$[0, 0, 0, -132, -144]$	$y^2=x^3-132x-144$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-8, 20)]$
5760.bq2	5760h1	5760.bq	5760h	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 $	$ 2^{7} \cdot 3^{9} \cdot 5^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1$	$1$	$1$	$1536$	$0.455669$	$1149984/625$	$1.24048$	$3.31399$	$[0, 0, 0, -297, 486]$	$y^2=x^3-297x+486$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[ ]$
28800.w2	28800ci1	28800.w	28800ci	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} $	$ 2^{7} \cdot 3^{9} \cdot 5^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1$	$1$	$1$	$36864$	$1.260387$	$1149984/625$	$1.24048$	$3.73500$	$[0, 0, 0, -7425, 60750]$	$y^2=x^3-7425x+60750$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[ ]$
28800.x2	28800j1	28800.x	28800j	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} $	$ 2^{7} \cdot 3^{3} \cdot 5^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$2.585286021$	$1$	$1$	$12288$	$0.711082$	$1149984/625$	$1.24048$	$3.09304$	$[0, 0, 0, -825, -2250]$	$y^2=x^3-825x-2250$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-15/2, 225/2)]$
28800.y1	28800i2	28800.y	28800i	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} $	$ 2^{13} \cdot 3^{3} \cdot 5^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1.829769968$	$1$	$3$	$24576$	$1.057655$	$1149984/625$	$1.24048$	$3.49807$	$[0, 0, 0, -3300, -18000]$	$y^2=x^3-3300x-18000$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-20, 200)]$
28800.z1	28800ch2	28800.z	28800ch	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} $	$ 2^{13} \cdot 3^{9} \cdot 5^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1$	$1$	$1$	$73728$	$1.606962$	$1149984/625$	$1.24048$	$4.14002$	$[0, 0, 0, -29700, 486000]$	$y^2=x^3-29700x+486000$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[ ]$
28800.de2	28800f1	28800.de	28800f	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} $	$ 2^{7} \cdot 3^{9} \cdot 5^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$5.210675971$	$1$	$1$	$36864$	$1.260387$	$1149984/625$	$1.24048$	$3.73500$	$[0, 0, 0, -7425, -60750]$	$y^2=x^3-7425x-60750$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-470/3, 11600/3)]$
28800.df2	28800ce1	28800.df	28800ce	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} $	$ 2^{7} \cdot 3^{3} \cdot 5^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1$	$1$	$1$	$12288$	$0.711082$	$1149984/625$	$1.24048$	$3.09304$	$[0, 0, 0, -825, 2250]$	$y^2=x^3-825x+2250$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[ ]$
28800.dg1	28800e2	28800.dg	28800e	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} $	$ 2^{13} \cdot 3^{3} \cdot 5^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1.100672056$	$1$	$7$	$24576$	$1.057655$	$1149984/625$	$1.24048$	$3.49807$	$[0, 0, 0, -3300, 18000]$	$y^2=x^3-3300x+18000$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-30, 300)]$
28800.dh1	28800cd2	28800.dh	28800cd	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} $	$ 2^{13} \cdot 3^{9} \cdot 5^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1$	$1$	$1$	$73728$	$1.606962$	$1149984/625$	$1.24048$	$4.14002$	$[0, 0, 0, -29700, -486000]$	$y^2=x^3-29700x-486000$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[ ]$
282240.ck2	282240ck1	282240.ck	282240ck	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ 2^{7} \cdot 3^{9} \cdot 5^{4} \cdot 7^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1$	$1$	$1$	$552960$	$1.428623$	$1149984/625$	$1.24048$	$3.21662$	$[0, 0, 0, -14553, -166698]$	$y^2=x^3-14553x-166698$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[ ]$
282240.cl2	282240cl1	282240.cl	282240cl	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ 2^{7} \cdot 3^{9} \cdot 5^{4} \cdot 7^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$6.835080806$	$1$	$1$	$552960$	$1.428623$	$1149984/625$	$1.24048$	$3.21662$	$[0, 0, 0, -14553, 166698]$	$y^2=x^3-14553x+166698$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-311/6, 116675/6)]$
282240.cx1	282240cx2	282240.cx	282240cx	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ 2^{13} \cdot 3^{3} \cdot 5^{4} \cdot 7^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1.418861551$	$1$	$7$	$368640$	$1.225891$	$1149984/625$	$1.24048$	$3.02278$	$[0, 0, 0, -6468, -49392]$	$y^2=x^3-6468x-49392$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-66, 300)]$
282240.cy1	282240cy2	282240.cy	282240cy	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ 2^{13} \cdot 3^{3} \cdot 5^{4} \cdot 7^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$3.096441722$	$1$	$5$	$368640$	$1.225891$	$1149984/625$	$1.24048$	$3.02278$	$[0, 0, 0, -6468, 49392]$	$y^2=x^3-6468x+49392$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-59, 475)]$
282240.hl2	282240hl1	282240.hl	282240hl	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ 2^{7} \cdot 3^{3} \cdot 5^{4} \cdot 7^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1$	$1$	$1$	$184320$	$0.879318$	$1149984/625$	$1.24048$	$2.69141$	$[0, 0, 0, -1617, 6174]$	$y^2=x^3-1617x+6174$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[ ]$
282240.hm2	282240hm1	282240.hm	282240hm	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ 2^{7} \cdot 3^{3} \cdot 5^{4} \cdot 7^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$2.751340058$	$1$	$3$	$184320$	$0.879318$	$1149984/625$	$1.24048$	$2.69141$	$[0, 0, 0, -1617, -6174]$	$y^2=x^3-1617x-6174$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-38, 20)]$
282240.ia1	282240ia2	282240.ia	282240ia	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ 2^{13} \cdot 3^{9} \cdot 5^{4} \cdot 7^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1.588274640$	$1$	$7$	$1105920$	$1.775198$	$1149984/625$	$1.24048$	$3.54799$	$[0, 0, 0, -58212, 1333584]$	$y^2=x^3-58212x+1333584$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(18, 540)]$
282240.ib1	282240ib2	282240.ib	282240ib	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ 2^{13} \cdot 3^{9} \cdot 5^{4} \cdot 7^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$3.643449633$	$1$	$3$	$1105920$	$1.775198$	$1149984/625$	$1.24048$	$3.54799$	$[0, 0, 0, -58212, -1333584]$	$y^2=x^3-58212x-1333584$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-68, 1520)]$
1411200.ln1	-	1411200.ln	-	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ 2^{13} \cdot 3^{3} \cdot 5^{10} \cdot 7^{6} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$5.084856877$	$1$	$13$	$8847360$	$2.030609$	$1149984/625$	$1.24048$	$3.36118$	$[0, 0, 0, -161700, -6174000]$	$y^2=x^3-161700x-6174000$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-80, 2500), (910, 24500)]$
1411200.lo1	-	1411200.lo	-	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ 2^{13} \cdot 3^{9} \cdot 5^{10} \cdot 7^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$3.080382855$	$1$	$3$	$26542080$	$2.579918$	$1149984/625$	$1.24048$	$3.82669$	$[0, 0, 0, -1455300, 166698000]$	$y^2=x^3-1455300x+166698000$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(1170, 8100)]$
1411200.lp1	-	1411200.lp	-	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ 2^{13} \cdot 3^{3} \cdot 5^{10} \cdot 7^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1$	$1$	$1$	$8847360$	$2.030609$	$1149984/625$	$1.24048$	$3.36118$	$[0, 0, 0, -161700, 6174000]$	$y^2=x^3-161700x+6174000$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[ ]$
1411200.lq1	-	1411200.lq	-	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ 2^{13} \cdot 3^{9} \cdot 5^{10} \cdot 7^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$9.274836043$	$1$	$1$	$26542080$	$2.579918$	$1149984/625$	$1.24048$	$3.82669$	$[0, 0, 0, -1455300, -166698000]$	$y^2=x^3-1455300x-166698000$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-35720/9, 14383900/9)]$
1411200.nv2	-	1411200.nv	-	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ 2^{7} \cdot 3^{9} \cdot 5^{10} \cdot 7^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$9.669022054$	$1$	$1$	$13271040$	$2.233341$	$1149984/625$	$1.24048$	$3.53298$	$[0, 0, 0, -363825, -20837250]$	$y^2=x^3-363825x-20837250$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-244730/23, 84702500/23)]$
1411200.nw2	-	1411200.nw	-	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ 2^{7} \cdot 3^{3} \cdot 5^{10} \cdot 7^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1$	$1$	$1$	$4423680$	$1.684036$	$1149984/625$	$1.24048$	$3.06747$	$[0, 0, 0, -40425, 771750]$	$y^2=x^3-40425x+771750$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[ ]$
1411200.nx2	-	1411200.nx	-	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ 2^{7} \cdot 3^{9} \cdot 5^{10} \cdot 7^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$1$	$1$	$1$	$13271040$	$2.233341$	$1149984/625$	$1.24048$	$3.53298$	$[0, 0, 0, -363825, 20837250]$	$y^2=x^3-363825x+20837250$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[ ]$
1411200.ny2	-	1411200.ny	-	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ 2^{7} \cdot 3^{3} \cdot 5^{10} \cdot 7^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.2	2B	$24$	$12$	$0$	$7.839797418$	$1$	$1$	$4423680$	$1.684036$	$1149984/625$	$1.24048$	$3.06747$	$[0, 0, 0, -40425, -771750]$	$y^2=x^3-40425x-771750$	2.3.0.a.1, 8.6.0.f.1, 12.6.0.b.1, 24.12.0.bl.1	$[(-8930/7, 252650/7)]$

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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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