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 (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
6930.i2	6930c2	6930.i	6930c	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{5} \cdot 3^{9} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1$	$1$	$0$	$15360$	$1.185854$	$61958108493/573927200$	$1.07326$	$4.23421$	$[1, -1, 0, 2226, -157132]$	$y^2+xy=x^3-x^2+2226x-157132$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[]$
6930.v2	6930s2	6930.v	6930s	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$0.156642577$	$1$	$14$	$5120$	$0.636547$	$61958108493/573927200$	$1.07326$	$3.48885$	$[1, -1, 1, 247, 5737]$	$y^2+xy+y=x^3-x^2+247x+5737$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(-5, 68)]$
34650.bx2	34650f2	34650.bx	34650f	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{5} \cdot 3^{3} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$0.636210143$	$1$	$8$	$122880$	$1.441265$	$61958108493/573927200$	$1.07326$	$3.87549$	$[1, -1, 0, 6183, 723341]$	$y^2+xy=x^3-x^2+6183x+723341$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(29, 948)]$
34650.dt2	34650co2	34650.dt	34650co	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{5} \cdot 3^{9} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1.393831698$	$1$	$6$	$368640$	$1.990572$	$61958108493/573927200$	$1.07326$	$4.50609$	$[1, -1, 1, 55645, -19585853]$	$y^2+xy+y=x^3-x^2+55645x-19585853$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(439, 9230)]$
48510.d2	48510b2	48510.d	48510b	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{5} \cdot 3^{9} \cdot 5^{2} \cdot 7^{8} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1$	$1$	$0$	$737280$	$2.158810$	$61958108493/573927200$	$1.07326$	$4.55267$	$[1, -1, 0, 109065, 53678141]$	$y^2+xy=x^3-x^2+109065x+53678141$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[]$
48510.dx2	48510ch2	48510.dx	48510ch	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7^{8} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$0.545137042$	$1$	$8$	$245760$	$1.609503$	$61958108493/573927200$	$1.07326$	$3.94174$	$[1, -1, 1, 12118, -1992119]$	$y^2+xy+y=x^3-x^2+12118x-1992119$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(191, 2599)]$
55440.bs2	55440ca2	55440.bs	55440ca	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1.227861522$	$1$	$7$	$122880$	$1.329695$	$61958108493/573927200$	$1.07326$	$3.58616$	$[0, 0, 0, 3957, -371142]$	$y^2=x^3+3957x-371142$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(69, 480)]$
55440.ew2	55440co2	55440.ew	55440co	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3^{9} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1.828943654$	$1$	$5$	$368640$	$1.879000$	$61958108493/573927200$	$1.07326$	$4.18962$	$[0, 0, 0, 35613, 10020834]$	$y^2=x^3+35613x+10020834$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(135, 4158)]$
76230.t2	76230d2	76230.t	76230d	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \cdot 11^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$2.811902555$	$1$	$4$	$614400$	$1.835495$	$61958108493/573927200$	$1.07326$	$4.02450$	$[1, -1, 0, 29925, -7726075]$	$y^2+xy=x^3-x^2+29925x-7726075$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(157, 829)]$
76230.es2	76230db2	76230.es	76230db	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{5} \cdot 3^{9} \cdot 5^{2} \cdot 7^{2} \cdot 11^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1.823124783$	$1$	$6$	$1843200$	$2.384800$	$61958108493/573927200$	$1.07326$	$4.61087$	$[1, -1, 1, 269323, 208334701]$	$y^2+xy+y=x^3-x^2+269323x+208334701$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(-349, 8644)]$
221760.cf2	221760nq2	221760.cf	221760nq	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{23} \cdot 3^{9} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$3.302384299$	$1$	$19$	$2949120$	$2.225574$	$61958108493/573927200$	$1.07326$	$4.05565$	$[0, 0, 0, 142452, -80166672]$	$y^2=x^3+142452x-80166672$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(478, 9856), (621, 15741)]$
221760.dt2	221760ha2	221760.dt	221760ha	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{23} \cdot 3^{9} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$2.003773018$	$1$	$3$	$2949120$	$2.225574$	$61958108493/573927200$	$1.07326$	$4.05565$	$[0, 0, 0, 142452, 80166672]$	$y^2=x^3+142452x+80166672$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(162, 10368)]$
221760.gw2	221760ne2	221760.gw	221760ne	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{23} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1$	$1$	$1$	$983040$	$1.676268$	$61958108493/573927200$	$1.07326$	$3.52015$	$[0, 0, 0, 15828, 2969136]$	$y^2=x^3+15828x+2969136$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[]$
221760.mv2	221760fq2	221760.mv	221760fq	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{23} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$2.802898632$	$1$	$5$	$983040$	$1.676268$	$61958108493/573927200$	$1.07326$	$3.52015$	$[0, 0, 0, 15828, -2969136]$	$y^2=x^3+15828x-2969136$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(240, 3828)]$
242550.go2	242550go2	242550.go	242550go	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{5} \cdot 3^{3} \cdot 5^{8} \cdot 7^{8} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1.804351538$	$1$	$6$	$5898240$	$2.414223$	$61958108493/573927200$	$1.07326$	$4.20891$	$[1, -1, 0, 302958, -248711884]$	$y^2+xy=x^3-x^2+302958x-248711884$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(779, 21048)]$
242550.kd2	242550kd2	242550.kd	242550kd	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{5} \cdot 3^{9} \cdot 5^{8} \cdot 7^{8} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1.866414171$	$1$	$6$	$17694720$	$2.963528$	$61958108493/573927200$	$1.07326$	$4.74054$	$[1, -1, 1, 2726620, 6712494247]$	$y^2+xy+y=x^3-x^2+2726620x+6712494247$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(65, 82973)]$
277200.z2	277200z2	277200.z	277200z	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3^{3} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1$	$1$	$1$	$2949120$	$2.134415$	$61958108493/573927200$	$1.07326$	$3.89615$	$[0, 0, 0, 98925, -46392750]$	$y^2=x^3+98925x-46392750$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[]$
277200.en2	277200en2	277200.en	277200en	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3^{9} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1.084581230$	$1$	$9$	$8847360$	$2.683720$	$61958108493/573927200$	$1.07326$	$4.42211$	$[0, 0, 0, 890325, 1252604250]$	$y^2=x^3+890325x+1252604250$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(565, 44000)]$
381150.dd2	381150dd2	381150.dd	381150dd	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{5} \cdot 3^{9} \cdot 5^{8} \cdot 7^{2} \cdot 11^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1$	$1$	$0$	$44236800$	$3.189518$	$61958108493/573927200$	$1.07326$	$4.78484$	$[1, -1, 0, 6733083, 26048570741]$	$y^2+xy=x^3-x^2+6733083x+26048570741$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[]$
381150.lo2	381150lo2	381150.lo	381150lo	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{5} \cdot 3^{3} \cdot 5^{8} \cdot 7^{2} \cdot 11^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$2.179865583$	$1$	$2$	$14745600$	$2.640213$	$61958108493/573927200$	$1.07326$	$4.27191$	$[1, -1, 1, 748120, -965011253]$	$y^2+xy+y=x^3-x^2+748120x-965011253$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(2599, 134825)]$
388080.fc2	388080fc2	388080.fc	388080fc	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{17} \cdot 3^{9} \cdot 5^{2} \cdot 7^{8} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$1$	$1$	$1$	$17694720$	$2.851955$	$61958108493/573927200$	$1.07326$	$4.46337$	$[0, 0, 0, 1745037, -3437146062]$	$y^2=x^3+1745037x-3437146062$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[]$
388080.ir2	388080ir2	388080.ir	388080ir	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{17} \cdot 3^{3} \cdot 5^{2} \cdot 7^{8} \cdot 11^{4} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$840$	$12$	$0$	$3.118756522$	$1$	$15$	$5898240$	$2.302650$	$61958108493/573927200$	$1.07326$	$3.95116$	$[0, 0, 0, 193893, 127301706]$	$y^2=x^3+193893x+127301706$	2.3.0.a.1, 24.6.0.b.1, 280.6.0.?, 420.6.0.?, 840.12.0.?	$[(-35, 10976), (6237, 493920)]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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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