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 (26 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
2790.g2	2790f1	2790.g	2790f	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 31 $	$ - 2^{7} \cdot 3^{3} \cdot 5^{3} \cdot 31^{3} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$3720$	$16$	$0$	$1.572770187$	$1$	$8$	$2016$	$0.628650$	$722458663317/476656000$	$0.97492$	$3.85714$	$[1, -1, 0, 561, 1773]$	$y^2+xy=x^3-x^2+561x+1773$	3.8.0-3.a.1.2, 3720.16.0.?	$[(-3, 9)]$
2790.q2	2790q2	2790.q	2790q	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 31 $	$ - 2^{7} \cdot 3^{9} \cdot 5^{3} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$3720$	$16$	$0$	$0.254623768$	$1$	$8$	$6048$	$1.177956$	$722458663317/476656000$	$0.97492$	$4.68797$	$[1, -1, 1, 5047, -52919]$	$y^2+xy+y=x^3-x^2+5047x-52919$	3.8.0-3.a.1.1, 3720.16.0.?	$[(73, 800)]$
13950.bb2	13950h2	13950.bb	13950h	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{7} \cdot 3^{9} \cdot 5^{9} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1$	$1$	$0$	$145152$	$1.982676$	$722458663317/476656000$	$0.97492$	$4.90924$	$[1, -1, 0, 126183, -6488659]$	$y^2+xy=x^3-x^2+126183x-6488659$	3.4.0.a.1, 15.8.0-3.a.1.1, 744.8.0.?, 3720.16.0.?	$[]$
13950.co2	13950bx1	13950.co	13950bx	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{7} \cdot 3^{3} \cdot 5^{9} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$0.123590948$	$1$	$8$	$48384$	$1.433369$	$722458663317/476656000$	$0.97492$	$4.21853$	$[1, -1, 1, 14020, 235647]$	$y^2+xy+y=x^3-x^2+14020x+235647$	3.4.0.a.1, 15.8.0-3.a.1.2, 744.8.0.?, 3720.16.0.?	$[(809, 22845)]$
22320.p2	22320t2	22320.p	22320t	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 31 $	$ - 2^{19} \cdot 3^{9} \cdot 5^{3} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1$	$1$	$0$	$145152$	$1.871103$	$722458663317/476656000$	$0.97492$	$4.54510$	$[0, 0, 0, 80757, 3306042]$	$y^2=x^3+80757x+3306042$	3.4.0.a.1, 12.8.0-3.a.1.2, 3720.16.0.?	$[]$
22320.bw2	22320z1	22320.bw	22320z	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 31 $	$ - 2^{19} \cdot 3^{3} \cdot 5^{3} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$0.717918920$	$1$	$4$	$48384$	$1.321796$	$722458663317/476656000$	$0.97492$	$3.88681$	$[0, 0, 0, 8973, -122446]$	$y^2=x^3+8973x-122446$	3.4.0.a.1, 12.8.0-3.a.1.1, 3720.16.0.?	$[(73, 960)]$
86490.y2	86490i1	86490.y	86490i	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 31^{2} $	$ - 2^{7} \cdot 3^{3} \cdot 5^{3} \cdot 31^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1.736969794$	$1$	$2$	$1935360$	$2.345642$	$722458663317/476656000$	$0.97492$	$4.50446$	$[1, -1, 0, 538941, -57131435]$	$y^2+xy=x^3-x^2+538941x-57131435$	3.4.0.a.1, 93.8.0.?, 120.8.0.?, 3720.16.0.?	$[(3635, 221615)]$
86490.bw2	86490bw2	86490.bw	86490bw	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 31^{2} $	$ - 2^{7} \cdot 3^{9} \cdot 5^{3} \cdot 31^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$2.119340101$	$1$	$0$	$5806080$	$2.894951$	$722458663317/476656000$	$0.97492$	$5.08431$	$[1, -1, 1, 4850467, 1537698277]$	$y^2+xy+y=x^3-x^2+4850467x+1537698277$	3.4.0.a.1, 93.8.0.?, 120.8.0.?, 3720.16.0.?	$[(-4481/5, 3228568/5)]$
89280.y2	89280j1	89280.y	89280j	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 31 $	$ - 2^{25} \cdot 3^{3} \cdot 5^{3} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1$	$1$	$0$	$387072$	$1.668371$	$722458663317/476656000$	$0.97492$	$3.77896$	$[0, 0, 0, 35892, 979568]$	$y^2=x^3+35892x+979568$	3.4.0.a.1, 24.8.0-3.a.1.2, 1860.8.0.?, 3720.16.0.?	$[]$
89280.bx2	89280dc1	89280.bx	89280dc	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 31 $	$ - 2^{25} \cdot 3^{3} \cdot 5^{3} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1$	$1$	$0$	$387072$	$1.668371$	$722458663317/476656000$	$0.97492$	$3.77896$	$[0, 0, 0, 35892, -979568]$	$y^2=x^3+35892x-979568$	3.4.0.a.1, 24.8.0-3.a.1.4, 930.8.0.?, 3720.16.0.?	$[]$
89280.dz2	89280v2	89280.dz	89280v	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 31 $	$ - 2^{25} \cdot 3^{9} \cdot 5^{3} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$0.596057016$	$1$	$4$	$1161216$	$2.217678$	$722458663317/476656000$	$0.97492$	$4.35720$	$[0, 0, 0, 323028, -26448336]$	$y^2=x^3+323028x-26448336$	3.4.0.a.1, 24.8.0-3.a.1.1, 1860.8.0.?, 3720.16.0.?	$[(1078, 39680)]$
89280.fb2	89280do2	89280.fb	89280do	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 31 $	$ - 2^{25} \cdot 3^{9} \cdot 5^{3} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$4.404530599$	$1$	$2$	$1161216$	$2.217678$	$722458663317/476656000$	$0.97492$	$4.35720$	$[0, 0, 0, 323028, 26448336]$	$y^2=x^3+323028x+26448336$	3.4.0.a.1, 24.8.0-3.a.1.3, 930.8.0.?, 3720.16.0.?	$[(2172, 104760)]$
111600.cq2	111600ck2	111600.cq	111600ck	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{19} \cdot 3^{9} \cdot 5^{9} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1$	$1$	$0$	$3483648$	$2.675823$	$722458663317/476656000$	$0.97492$	$4.74657$	$[0, 0, 0, 2018925, 413255250]$	$y^2=x^3+2018925x+413255250$	3.4.0.a.1, 60.8.0-3.a.1.1, 744.8.0.?, 3720.16.0.?	$[]$
111600.cy2	111600cj1	111600.cy	111600cj	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{19} \cdot 3^{3} \cdot 5^{9} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1$	$1$	$0$	$1161216$	$2.126514$	$722458663317/476656000$	$0.97492$	$4.17943$	$[0, 0, 0, 224325, -15305750]$	$y^2=x^3+224325x-15305750$	3.4.0.a.1, 60.8.0-3.a.1.2, 744.8.0.?, 3720.16.0.?	$[]$
136710.l2	136710gl1	136710.l	136710gl	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 31 $	$ - 2^{7} \cdot 3^{3} \cdot 5^{3} \cdot 7^{6} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$26040$	$16$	$0$	$1$	$1$	$0$	$762048$	$1.601604$	$722458663317/476656000$	$0.97492$	$3.57505$	$[1, -1, 0, 27480, -663104]$	$y^2+xy=x^3-x^2+27480x-663104$	3.4.0.a.1, 21.8.0-3.a.1.1, 3720.8.0.?, 26040.16.0.?	$[]$
136710.gl2	136710cm2	136710.gl	136710cm	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 31 $	$ - 2^{7} \cdot 3^{9} \cdot 5^{3} \cdot 7^{6} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$26040$	$16$	$0$	$1$	$1$	$0$	$2286144$	$2.150909$	$722458663317/476656000$	$0.97492$	$4.13246$	$[1, -1, 1, 247318, 17656489]$	$y^2+xy+y=x^3-x^2+247318x+17656489$	3.4.0.a.1, 21.8.0-3.a.1.2, 3720.8.0.?, 26040.16.0.?	$[]$
337590.be2	337590be2	337590.be	337590be	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 31 $	$ - 2^{7} \cdot 3^{9} \cdot 5^{3} \cdot 11^{6} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$40920$	$16$	$0$	$7.875726886$	$1$	$0$	$8164800$	$2.376904$	$722458663317/476656000$	$0.97492$	$4.05204$	$[1, -1, 0, 610725, 68602661]$	$y^2+xy=x^3-x^2+610725x+68602661$	3.4.0.a.1, 33.8.0-3.a.1.1, 3720.8.0.?, 40920.16.0.?	$[(58045/11, 28591151/11)]$
337590.fa2	337590fa1	337590.fa	337590fa	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 31 $	$ - 2^{7} \cdot 3^{3} \cdot 5^{3} \cdot 11^{6} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$40920$	$16$	$0$	$0.588291273$	$1$	$6$	$2721600$	$1.827597$	$722458663317/476656000$	$0.97492$	$3.53422$	$[1, -1, 1, 67858, -2563459]$	$y^2+xy+y=x^3-x^2+67858x-2563459$	3.4.0.a.1, 33.8.0-3.a.1.2, 3720.8.0.?, 40920.16.0.?	$[(81, 1819)]$
432450.cg2	432450cg2	432450.cg	432450cg	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ - 2^{7} \cdot 3^{9} \cdot 5^{9} \cdot 31^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1$	$1$	$0$	$139345920$	$3.699669$	$722458663317/476656000$	$0.97492$	$5.19788$	$[1, -1, 0, 121261683, 192333546341]$	$y^2+xy=x^3-x^2+121261683x+192333546341$	3.4.0.a.1, 24.8.0-3.a.1.8, 465.8.0.?, 3720.16.0.?	$[]$
432450.gw2	432450gw1	432450.gw	432450gw	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ - 2^{7} \cdot 3^{3} \cdot 5^{9} \cdot 31^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1.187471093$	$1$	$0$	$46448640$	$3.150364$	$722458663317/476656000$	$0.97492$	$4.68993$	$[1, -1, 1, 13473520, -7127955853]$	$y^2+xy+y=x^3-x^2+13473520x-7127955853$	3.4.0.a.1, 24.8.0-3.a.1.7, 465.8.0.?, 3720.16.0.?	$[(14611/3, 3701945/3)]$
446400.gm2	446400gm1	446400.gm	446400gm	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{25} \cdot 3^{3} \cdot 5^{9} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1$	$1$	$0$	$9289728$	$2.473091$	$722458663317/476656000$	$0.97492$	$4.05374$	$[0, 0, 0, 897300, -122446000]$	$y^2=x^3+897300x-122446000$	3.4.0.a.1, 120.8.0.?, 186.8.0.?, 3720.16.0.?	$[]$
446400.hb2	446400hb2	446400.hb	446400hb	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{25} \cdot 3^{9} \cdot 5^{9} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1$	$1$	$0$	$27869184$	$3.022396$	$722458663317/476656000$	$0.97492$	$4.56045$	$[0, 0, 0, 8075700, 3306042000]$	$y^2=x^3+8075700x+3306042000$	3.4.0.a.1, 120.8.0.?, 186.8.0.?, 3720.16.0.?	$[]$
446400.mp2	446400mp2	446400.mp	446400mp	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{25} \cdot 3^{9} \cdot 5^{9} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1$	$1$	$0$	$27869184$	$3.022396$	$722458663317/476656000$	$0.97492$	$4.56045$	$[0, 0, 0, 8075700, -3306042000]$	$y^2=x^3+8075700x-3306042000$	3.4.0.a.1, 120.8.0.?, 372.8.0.?, 3720.16.0.?	$[]$
446400.nc2	446400nc1	446400.nc	446400nc	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{25} \cdot 3^{3} \cdot 5^{9} \cdot 31^{3} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$2.900354957$	$1$	$10$	$9289728$	$2.473091$	$722458663317/476656000$	$0.97492$	$4.05374$	$[0, 0, 0, 897300, 122446000]$	$y^2=x^3+897300x+122446000$	3.4.0.a.1, 120.8.0.?, 372.8.0.?, 3720.16.0.?	$[(-40, 9300), (-90, 6400)]$
471510.cc2	471510cc2	471510.cc	471510cc	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \cdot 31 $	$ - 2^{7} \cdot 3^{9} \cdot 5^{3} \cdot 13^{6} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$48360$	$16$	$0$	$1$	$1$	$0$	$13063680$	$2.460430$	$722458663317/476656000$	$0.97492$	$4.02513$	$[1, -1, 0, 852996, -113703472]$	$y^2+xy=x^3-x^2+852996x-113703472$	3.4.0.a.1, 39.8.0-3.a.1.2, 3720.8.0.?, 48360.16.0.?	$[]$
471510.dl2	471510dl1	471510.dl	471510dl	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \cdot 31 $	$ - 2^{7} \cdot 3^{3} \cdot 5^{3} \cdot 13^{6} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$48360$	$16$	$0$	$1$	$1$	$0$	$4354560$	$1.911125$	$722458663317/476656000$	$0.97492$	$3.52056$	$[1, -1, 1, 94777, 4179647]$	$y^2+xy+y=x^3-x^2+94777x+4179647$	3.4.0.a.1, 39.8.0-3.a.1.1, 3720.8.0.?, 48360.16.0.?	$[]$

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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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