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 (23 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
4488.k3	4488e2	4488.k	4488e	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{6} \cdot 11^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2244$	$48$	$0$	$1$	$1$	$3$	$2304$	$0.576333$	$51553893328/25492401$	$0.90082$	$3.59264$	$[0, 1, 0, -492, 1440]$	$y^2=x^3+x^2-492x+1440$	2.6.0.a.1, 12.12.0-2.a.1.1, 44.12.0-2.a.1.1, 68.12.0-2.a.1.1, 132.24.0.?, $\ldots$	$[]$
8976.o3	8976e2	8976.o	8976e	$4$	$4$	$ 2^{4} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{6} \cdot 11^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2244$	$48$	$0$	$1$	$1$	$3$	$4608$	$0.576333$	$51553893328/25492401$	$0.90082$	$3.31906$	$[0, -1, 0, -492, -1440]$	$y^2=x^3-x^2-492x-1440$	2.6.0.a.1, 12.12.0-2.a.1.1, 44.12.0-2.a.1.1, 68.12.0-2.a.1.1, 132.24.0.?, $\ldots$	$[]$
13464.g3	13464v2	13464.g	13464v	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{12} \cdot 11^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2244$	$48$	$0$	$1.971818356$	$1$	$9$	$18432$	$1.125639$	$51553893328/25492401$	$0.90082$	$3.87081$	$[0, 0, 0, -4431, -43310]$	$y^2=x^3-4431x-43310$	2.6.0.a.1, 4.12.0-2.a.1.1, 132.24.0.?, 204.24.0.?, 748.24.0.?, $\ldots$	$[(-27, 238)]$
26928.k3	26928p2	26928.k	26928p	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{12} \cdot 11^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2244$	$48$	$0$	$2.185413387$	$1$	$9$	$36864$	$1.125639$	$51553893328/25492401$	$0.90082$	$3.60779$	$[0, 0, 0, -4431, 43310]$	$y^2=x^3-4431x+43310$	2.6.0.a.1, 4.12.0-2.a.1.1, 132.24.0.?, 204.24.0.?, 748.24.0.?, $\ldots$	$[(-7, 272)]$
35904.n3	35904s2	35904.n	35904s	$4$	$4$	$ 2^{6} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{14} \cdot 3^{6} \cdot 11^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$4488$	$48$	$0$	$1$	$1$	$3$	$36864$	$0.922907$	$51553893328/25492401$	$0.90082$	$3.27689$	$[0, -1, 0, -1969, 13489]$	$y^2=x^3-x^2-1969x+13489$	2.6.0.a.1, 24.12.0-2.a.1.1, 88.12.0.?, 132.12.0.?, 136.12.0.?, $\ldots$	$[]$
35904.bv3	35904cm2	35904.bv	35904cm	$4$	$4$	$ 2^{6} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{14} \cdot 3^{6} \cdot 11^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$4488$	$48$	$0$	$1.046803489$	$1$	$13$	$36864$	$0.922907$	$51553893328/25492401$	$0.90082$	$3.27689$	$[0, 1, 0, -1969, -13489]$	$y^2=x^3+x^2-1969x-13489$	2.6.0.a.1, 24.12.0-2.a.1.1, 88.12.0.?, 132.12.0.?, 136.12.0.?, $\ldots$	$[(95, 816)]$
49368.bh3	49368bk2	49368.bh	49368bk	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11^{2} \cdot 17 $	$ 2^{8} \cdot 3^{6} \cdot 11^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2244$	$48$	$0$	$1.920434756$	$1$	$9$	$276480$	$1.775280$	$51553893328/25492401$	$0.90082$	$4.12679$	$[0, 1, 0, -59572, -2154880]$	$y^2=x^3+x^2-59572x-2154880$	2.6.0.a.1, 4.12.0-2.a.1.1, 132.24.0.?, 204.24.0.?, 748.24.0.?, $\ldots$	$[(326, 3630)]$
76296.c3	76296c2	76296.c	76296c	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17^{2} $	$ 2^{8} \cdot 3^{6} \cdot 11^{2} \cdot 17^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2244$	$48$	$0$	$1$	$1$	$3$	$663552$	$1.992941$	$51553893328/25492401$	$0.90082$	$4.19932$	$[0, -1, 0, -142284, 7928244]$	$y^2=x^3-x^2-142284x+7928244$	2.6.0.a.1, 4.12.0-2.a.1.1, 132.24.0.?, 204.24.0.?, 748.24.0.?, $\ldots$	$[]$
98736.cb3	98736q2	98736.cb	98736q	$4$	$4$	$ 2^{4} \cdot 3 \cdot 11^{2} \cdot 17 $	$ 2^{8} \cdot 3^{6} \cdot 11^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2244$	$48$	$0$	$12.02551971$	$1$	$3$	$552960$	$1.775280$	$51553893328/25492401$	$0.90082$	$3.87806$	$[0, -1, 0, -59572, 2154880]$	$y^2=x^3-x^2-59572x+2154880$	2.6.0.a.1, 4.12.0-2.a.1.1, 132.24.0.?, 204.24.0.?, 748.24.0.?, $\ldots$	$[(-744644/63, 646860880/63)]$
107712.dm3	107712fa2	107712.dm	107712fa	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{14} \cdot 3^{12} \cdot 11^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$4488$	$48$	$0$	$3.795091673$	$1$	$5$	$294912$	$1.472214$	$51553893328/25492401$	$0.90082$	$3.53507$	$[0, 0, 0, -17724, 346480]$	$y^2=x^3-17724x+346480$	2.6.0.a.1, 8.12.0-2.a.1.1, 132.12.0.?, 204.12.0.?, 264.24.0.?, $\ldots$	$[(-78, 1120)]$
107712.eh3	107712bm2	107712.eh	107712bm	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{14} \cdot 3^{12} \cdot 11^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$4488$	$48$	$0$	$5.760230914$	$1$	$3$	$294912$	$1.472214$	$51553893328/25492401$	$0.90082$	$3.53507$	$[0, 0, 0, -17724, -346480]$	$y^2=x^3-17724x-346480$	2.6.0.a.1, 8.12.0-2.a.1.1, 132.12.0.?, 204.12.0.?, 264.24.0.?, $\ldots$	$[(3614/5, 41888/5)]$
112200.b3	112200bo2	112200.b	112200bo	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{6} \cdot 5^{6} \cdot 11^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$11220$	$48$	$0$	$1.116997450$	$1$	$13$	$294912$	$1.381052$	$51553893328/25492401$	$0.90082$	$3.42858$	$[0, -1, 0, -12308, 204612]$	$y^2=x^3-x^2-12308x+204612$	2.6.0.a.1, 60.12.0-2.a.1.1, 132.12.0.?, 204.12.0.?, 220.12.0.?, $\ldots$	$[(-8, 550)]$
148104.h3	148104bo2	148104.h	148104bo	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ 2^{8} \cdot 3^{12} \cdot 11^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2244$	$48$	$0$	$4.491841091$	$1$	$5$	$2211840$	$2.324589$	$51553893328/25492401$	$0.90082$	$4.29964$	$[0, 0, 0, -536151, 57645610]$	$y^2=x^3-536151x+57645610$	2.6.0.a.1, 12.12.0-2.a.1.1, 44.12.0-2.a.1.1, 68.12.0-2.a.1.2, 132.24.0.?, $\ldots$	$[(-706, 9180)]$
152592.cb3	152592cq2	152592.cb	152592cq	$4$	$4$	$ 2^{4} \cdot 3 \cdot 11 \cdot 17^{2} $	$ 2^{8} \cdot 3^{6} \cdot 11^{2} \cdot 17^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$2244$	$48$	$0$	$1$	$1$	$3$	$1327104$	$1.992941$	$51553893328/25492401$	$0.90082$	$3.95545$	$[0, 1, 0, -142284, -7928244]$	$y^2=x^3+x^2-142284x-7928244$	2.6.0.a.1, 4.12.0-2.a.1.1, 132.24.0.?, 204.24.0.?, 748.24.0.?, $\ldots$	$[]$
219912.f3	219912br2	219912.f	219912br	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{6} \cdot 7^{6} \cdot 11^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$15708$	$48$	$0$	$2.388537394$	$1$	$9$	$663552$	$1.549288$	$51553893328/25492401$	$0.90082$	$3.40514$	$[0, -1, 0, -24124, -542156]$	$y^2=x^3-x^2-24124x-542156$	2.6.0.a.1, 84.12.0.?, 132.12.0.?, 204.12.0.?, 308.12.0.?, $\ldots$	$[(-30, 392)]$
224400.il3	224400he2	224400.il	224400he	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{6} \cdot 5^{6} \cdot 11^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$11220$	$48$	$0$	$1$	$1$	$3$	$589824$	$1.381052$	$51553893328/25492401$	$0.90082$	$3.23570$	$[0, 1, 0, -12308, -204612]$	$y^2=x^3+x^2-12308x-204612$	2.6.0.a.1, 60.12.0-2.a.1.1, 132.12.0.?, 204.12.0.?, 220.12.0.?, $\ldots$	$[]$
228888.bv3	228888s2	228888.bv	228888s	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 11 \cdot 17^{2} $	$ 2^{8} \cdot 3^{12} \cdot 11^{2} \cdot 17^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2244$	$48$	$0$	$5.567504324$	$1$	$3$	$5308416$	$2.542248$	$51553893328/25492401$	$0.90082$	$4.35962$	$[0, 0, 0, -1280559, -212782030]$	$y^2=x^3-1280559x-212782030$	2.6.0.a.1, 12.12.0-2.a.1.1, 44.12.0-2.a.1.2, 68.12.0-2.a.1.1, 132.24.0.?, $\ldots$	$[(-3587/3, 413270/3)]$
296208.bs3	296208bs2	296208.bs	296208bs	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ 2^{8} \cdot 3^{12} \cdot 11^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2244$	$48$	$0$	$12.19839806$	$1$	$3$	$4423680$	$2.324589$	$51553893328/25492401$	$0.90082$	$4.06309$	$[0, 0, 0, -536151, -57645610]$	$y^2=x^3-536151x-57645610$	2.6.0.a.1, 12.12.0-2.a.1.1, 44.12.0-2.a.1.1, 68.12.0-2.a.1.2, 132.24.0.?, $\ldots$	$[(6124693/13, 15154358688/13)]$
336600.j3	336600j2	336600.j	336600j	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{12} \cdot 5^{6} \cdot 11^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$11220$	$48$	$0$	$3.104185888$	$1$	$7$	$2359296$	$1.930359$	$51553893328/25492401$	$0.90082$	$3.65056$	$[0, 0, 0, -110775, -5413750]$	$y^2=x^3-110775x-5413750$	2.6.0.a.1, 20.12.0-2.a.1.1, 132.12.0.?, 204.12.0.?, 660.24.0.?, $\ldots$	$[(575, 11000)]$
394944.l3	394944l2	394944.l	394944l	$4$	$4$	$ 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 $	$ 2^{14} \cdot 3^{6} \cdot 11^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$4488$	$48$	$0$	$4.121844904$	$1$	$5$	$4423680$	$2.121853$	$51553893328/25492401$	$0.90082$	$3.78360$	$[0, -1, 0, -238289, -17000751]$	$y^2=x^3-x^2-238289x-17000751$	2.6.0.a.1, 8.12.0-2.a.1.1, 132.12.0.?, 204.12.0.?, 264.24.0.?, $\ldots$	$[(777, 16320)]$
394944.fy3	394944fy2	394944.fy	394944fy	$4$	$4$	$ 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 $	$ 2^{14} \cdot 3^{6} \cdot 11^{8} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$4488$	$48$	$0$	$3.325333632$	$1$	$7$	$4423680$	$2.121853$	$51553893328/25492401$	$0.90082$	$3.78360$	$[0, 1, 0, -238289, 17000751]$	$y^2=x^3+x^2-238289x+17000751$	2.6.0.a.1, 8.12.0-2.a.1.1, 132.12.0.?, 204.12.0.?, 264.24.0.?, $\ldots$	$[(55, 2016)]$
439824.eb3	439824eb2	439824.eb	439824eb	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{6} \cdot 7^{6} \cdot 11^{2} \cdot 17^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$15708$	$48$	$0$	$1.842849741$	$1$	$9$	$1327104$	$1.549288$	$51553893328/25492401$	$0.90082$	$3.22350$	$[0, 1, 0, -24124, 542156]$	$y^2=x^3+x^2-24124x+542156$	2.6.0.a.1, 84.12.0.?, 132.12.0.?, 204.12.0.?, 308.12.0.?, $\ldots$	$[(170, 1176)]$
457776.fh3	457776fh2	457776.fh	457776fh	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 11 \cdot 17^{2} $	$ 2^{8} \cdot 3^{12} \cdot 11^{2} \cdot 17^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2244$	$48$	$0$	$19.67245265$	$1$	$3$	$10616832$	$2.542248$	$51553893328/25492401$	$0.90082$	$4.12778$	$[0, 0, 0, -1280559, 212782030]$	$y^2=x^3-1280559x+212782030$	2.6.0.a.1, 12.12.0-2.a.1.1, 44.12.0-2.a.1.2, 68.12.0-2.a.1.1, 132.24.0.?, $\ldots$	$[(1828143433/3297, 52860169170640/3297)]$

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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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