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 (22 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
4650.q2	4650v2	4650.q	4650v	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{9} \cdot 3^{2} \cdot 5^{8} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$744$	$16$	$0$	$1$	$1$	$0$	$12960$	$1.317236$	$36450495095/137276928$	$0.95530$	$4.60659$	$[1, 0, 1, 5049, -323702]$	$y^2+xy+y=x^3+5049x-323702$	3.8.0-3.a.1.1, 248.2.0.?, 744.16.0.?	$[ ]$
4650.bf2	4650ba2	4650.bf	4650ba	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{9} \cdot 3^{2} \cdot 5^{2} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$0.125744242$	$1$	$8$	$2592$	$0.512517$	$36450495095/137276928$	$0.95530$	$3.46306$	$[1, 1, 1, 202, -2509]$	$y^2+xy+y=x^3+x^2+202x-2509$	3.4.0.a.1, 15.8.0-3.a.1.1, 248.2.0.?, 744.8.0.?, 3720.16.0.?	$[(81, 703)]$
13950.x2	13950u2	13950.x	13950u	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{9} \cdot 3^{8} \cdot 5^{2} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$0.466140320$	$1$	$6$	$20736$	$1.061823$	$36450495095/137276928$	$0.95530$	$3.75512$	$[1, -1, 0, 1818, 69556]$	$y^2+xy=x^3-x^2+1818x+69556$	3.4.0.a.1, 15.8.0-3.a.1.2, 248.2.0.?, 744.8.0.?, 3720.16.0.?	$[(35, 401)]$
13950.ca2	13950cx2	13950.ca	13950cx	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{9} \cdot 3^{8} \cdot 5^{8} \cdot 31^{3} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$744$	$16$	$0$	$0.750361287$	$1$	$12$	$103680$	$1.866541$	$36450495095/137276928$	$0.95530$	$4.76700$	$[1, -1, 1, 45445, 8739947]$	$y^2+xy+y=x^3-x^2+45445x+8739947$	3.8.0-3.a.1.2, 248.2.0.?, 744.16.0.?	$[(219, 5290)]$
37200.bf2	37200cc2	37200.bf	37200cc	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{21} \cdot 3^{2} \cdot 5^{8} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$744$	$16$	$0$	$5.592726283$	$1$	$2$	$311040$	$2.010384$	$36450495095/137276928$	$0.95530$	$4.48673$	$[0, -1, 0, 80792, 20716912]$	$y^2=x^3-x^2+80792x+20716912$	3.4.0.a.1, 12.8.0-3.a.1.2, 248.2.0.?, 744.16.0.?	$[(73, 5196)]$
37200.cr2	37200cs2	37200.cr	37200cs	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{21} \cdot 3^{2} \cdot 5^{2} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1.526590482$	$1$	$2$	$62208$	$1.205664$	$36450495095/137276928$	$0.95530$	$3.56916$	$[0, 1, 0, 3232, 167028]$	$y^2=x^3+x^2+3232x+167028$	3.4.0.a.1, 60.8.0-3.a.1.1, 248.2.0.?, 744.8.0.?, 3720.16.0.?	$[(-6, 384)]$
111600.cx2	111600dq2	111600.cx	111600dq	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{21} \cdot 3^{8} \cdot 5^{2} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$3.734087326$	$1$	$2$	$497664$	$1.754971$	$36450495095/137276928$	$0.95530$	$3.79893$	$[0, 0, 0, 29085, -4480670]$	$y^2=x^3+29085x-4480670$	3.4.0.a.1, 60.8.0-3.a.1.2, 248.2.0.?, 744.8.0.?, 3720.16.0.?	$[(311, 5886)]$
111600.ey2	111600fs2	111600.ey	111600fs	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{21} \cdot 3^{8} \cdot 5^{8} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$744$	$16$	$0$	$1$	$1$	$0$	$2488320$	$2.559689$	$36450495095/137276928$	$0.95530$	$4.62977$	$[0, 0, 0, 727125, -560083750]$	$y^2=x^3+727125x-560083750$	3.4.0.a.1, 12.8.0-3.a.1.1, 248.2.0.?, 744.16.0.?	$[ ]$
144150.k2	144150ec2	144150.k	144150ec	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 31^{2} $	$ - 2^{9} \cdot 3^{2} \cdot 5^{8} \cdot 31^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$744$	$16$	$0$	$6.889983104$	$1$	$0$	$12441600$	$3.034229$	$36450495095/137276928$	$0.95530$	$5.00941$	$[1, 1, 0, 4852550, 9657956500]$	$y^2+xy=x^3+x^2+4852550x+9657956500$	3.4.0.a.1, 24.8.0-3.a.1.5, 93.8.0.?, 248.2.0.?, 744.16.0.?	$[(-18059/4, 3389047/4)]$
144150.eo2	144150t2	144150.eo	144150t	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 31^{2} $	$ - 2^{9} \cdot 3^{2} \cdot 5^{2} \cdot 31^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1$	$1$	$0$	$2488320$	$2.229511$	$36450495095/137276928$	$0.95530$	$4.19647$	$[1, 0, 0, 194102, 77263652]$	$y^2+xy=x^3+194102x+77263652$	3.4.0.a.1, 120.8.0.?, 248.2.0.?, 465.8.0.?, 744.8.0.?, $\ldots$	$[ ]$
148800.bw2	148800iw2	148800.bw	148800iw	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{27} \cdot 3^{2} \cdot 5^{8} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$744$	$16$	$0$	$1.162422748$	$1$	$2$	$2488320$	$2.356956$	$36450495095/137276928$	$0.95530$	$4.31369$	$[0, -1, 0, 323167, -166058463]$	$y^2=x^3-x^2+323167x-166058463$	3.4.0.a.1, 24.8.0-3.a.1.1, 186.8.0.?, 248.2.0.?, 744.16.0.?	$[(467, 9300)]$
148800.ce2	148800ep2	148800.ce	148800ep	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{27} \cdot 3^{2} \cdot 5^{2} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1$	$1$	$0$	$497664$	$1.552238$	$36450495095/137276928$	$0.95530$	$3.50291$	$[0, -1, 0, 12927, 1323297]$	$y^2=x^3-x^2+12927x+1323297$	3.4.0.a.1, 120.8.0.?, 248.2.0.?, 744.8.0.?, 1860.8.0.?, $\ldots$	$[ ]$
148800.jf2	148800hv2	148800.jf	148800hv	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{27} \cdot 3^{2} \cdot 5^{2} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$1.660841428$	$1$	$2$	$497664$	$1.552238$	$36450495095/137276928$	$0.95530$	$3.50291$	$[0, 1, 0, 12927, -1323297]$	$y^2=x^3+x^2+12927x-1323297$	3.4.0.a.1, 120.8.0.?, 248.2.0.?, 744.8.0.?, 930.8.0.?, $\ldots$	$[(267, 4608)]$
148800.ji2	148800s2	148800.ji	148800s	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 $	$ - 2^{27} \cdot 3^{2} \cdot 5^{8} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$744$	$16$	$0$	$1$	$1$	$0$	$2488320$	$2.356956$	$36450495095/137276928$	$0.95530$	$4.31369$	$[0, 1, 0, 323167, 166058463]$	$y^2=x^3+x^2+323167x+166058463$	3.4.0.a.1, 24.8.0-3.a.1.3, 248.2.0.?, 372.8.0.?, 744.16.0.?	$[ ]$
227850.bv2	227850ht2	227850.bv	227850ht	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 31 $	$ - 2^{9} \cdot 3^{2} \cdot 5^{8} \cdot 7^{6} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$5208$	$16$	$0$	$4.185038444$	$1$	$2$	$4898880$	$2.290192$	$36450495095/137276928$	$0.95530$	$4.09975$	$[1, 1, 0, 247425, 111277125]$	$y^2+xy=x^3+x^2+247425x+111277125$	3.4.0.a.1, 21.8.0-3.a.1.2, 248.2.0.?, 744.8.0.?, 5208.16.0.?	$[(435, 17145)]$
227850.jb2	227850ca2	227850.jb	227850ca	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 31 $	$ - 2^{9} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 31^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$26040$	$16$	$0$	$1$	$1$	$0$	$979776$	$1.485472$	$36450495095/137276928$	$0.95530$	$3.31698$	$[1, 0, 0, 9897, 890217]$	$y^2+xy=x^3+9897x+890217$	3.4.0.a.1, 105.8.0.?, 248.2.0.?, 744.8.0.?, 26040.16.0.?	$[ ]$
432450.cr2	432450cr2	432450.cr	432450cr	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ - 2^{9} \cdot 3^{8} \cdot 5^{2} \cdot 31^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$11.43095407$	$1$	$0$	$19906560$	$2.778816$	$36450495095/137276928$	$0.95530$	$4.34915$	$[1, -1, 0, 1746918, -2086118604]$	$y^2+xy=x^3-x^2+1746918x-2086118604$	3.4.0.a.1, 120.8.0.?, 248.2.0.?, 465.8.0.?, 744.8.0.?, $\ldots$	$[(475635/2, 327571233/2)]$
432450.fr2	432450fr2	432450.fr	432450fr	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ - 2^{9} \cdot 3^{8} \cdot 5^{8} \cdot 31^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$744$	$16$	$0$	$1.579791531$	$1$	$4$	$99532800$	$3.583534$	$36450495095/137276928$	$0.95530$	$5.09327$	$[1, -1, 1, 43672945, -260721152553]$	$y^2+xy+y=x^3-x^2+43672945x-260721152553$	3.4.0.a.1, 24.8.0-3.a.1.6, 93.8.0.?, 248.2.0.?, 744.16.0.?	$[(7169, 645090)]$
446400.gr2	446400gr2	446400.gr	446400gr	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{27} \cdot 3^{8} \cdot 5^{2} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$5.112313704$	$1$	$2$	$3981312$	$2.101543$	$36450495095/137276928$	$0.95530$	$3.71379$	$[0, 0, 0, 116340, -35845360]$	$y^2=x^3+116340x-35845360$	3.4.0.a.1, 120.8.0.?, 248.2.0.?, 744.8.0.?, 1860.8.0.?, $\ldots$	$[(1504, 59508)]$
446400.ha2	446400ha2	446400.ha	446400ha	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{27} \cdot 3^{8} \cdot 5^{8} \cdot 31^{3} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$744$	$16$	$0$	$3.706858186$	$1$	$10$	$19906560$	$2.906261$	$36450495095/137276928$	$0.95530$	$4.45610$	$[0, 0, 0, 2908500, 4480670000]$	$y^2=x^3+2908500x+4480670000$	3.4.0.a.1, 24.8.0-3.a.1.2, 186.8.0.?, 248.2.0.?, 744.16.0.?	$[(2134, 142848), (-284, 60264)]$
446400.mo2	446400mo2	446400.mo	446400mo	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{27} \cdot 3^{8} \cdot 5^{8} \cdot 31^{3} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$744$	$16$	$0$	$15.12509417$	$1$	$6$	$19906560$	$2.906261$	$36450495095/137276928$	$0.95530$	$4.45610$	$[0, 0, 0, 2908500, -4480670000]$	$y^2=x^3+2908500x-4480670000$	3.4.0.a.1, 24.8.0-3.a.1.4, 248.2.0.?, 372.8.0.?, 744.16.0.?	$[(2474, 133632), (17834, 2391552)]$
446400.nh2	446400nh2	446400.nh	446400nh	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{27} \cdot 3^{8} \cdot 5^{2} \cdot 31^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3720$	$16$	$0$	$2.387450071$	$1$	$2$	$3981312$	$2.101543$	$36450495095/137276928$	$0.95530$	$3.71379$	$[0, 0, 0, 116340, 35845360]$	$y^2=x^3+116340x+35845360$	3.4.0.a.1, 120.8.0.?, 248.2.0.?, 744.8.0.?, 930.8.0.?, $\ldots$	$[(836, 26784)]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 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.

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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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