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 (20 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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
2440.d1	2440d1	2440.d	2440d	$2$	$2$	$ 2^{3} \cdot 5 \cdot 61 $	$ 2^{8} \cdot 5 \cdot 61 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.21	2B	$2440$	$48$	$0$	$1$	$1$		$1$	$384$	$-0.124728$	$436334416/305$	$0.78613$	$3.26153$	$[0, -1, 0, -100, 420]$	$y^2=x^3-x^2-100x+420$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 610.6.0.?, 1220.24.0.?, $\ldots$	$[]$
4880.a1	4880d1	4880.a	4880d	$2$	$2$	$ 2^{4} \cdot 5 \cdot 61 $	$ 2^{8} \cdot 5 \cdot 61 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.21	2B	$2440$	$48$	$0$	$3.223494506$	$1$		$3$	$768$	$-0.124728$	$436334416/305$	$0.78613$	$2.99534$	$[0, 1, 0, -100, -420]$	$y^2=x^3+x^2-100x-420$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 610.6.0.?, 1220.24.0.?, $\ldots$	$[(19, 70)]$
12200.a1	12200b1	12200.a	12200b	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 61 $	$ 2^{8} \cdot 5^{7} \cdot 61 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$2440$	$48$	$0$	$1.444840237$	$1$		$15$	$9216$	$0.679991$	$436334416/305$	$0.78613$	$3.72994$	$[0, 1, 0, -2508, 47488]$	$y^2=x^3+x^2-2508x+47488$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.3, 488.12.0.?, 610.6.0.?, $\ldots$	$[(23, 50), (-52, 200)]$
19520.b1	19520e1	19520.b	19520e	$2$	$2$	$ 2^{6} \cdot 5 \cdot 61 $	$ 2^{14} \cdot 5 \cdot 61 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.22	2B	$2440$	$48$	$0$	$1.768309285$	$1$		$5$	$6144$	$0.221845$	$436334416/305$	$0.78613$	$2.99599$	$[0, 1, 0, -401, 2959]$	$y^2=x^3+x^2-401x+2959$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 610.6.0.?, 1220.24.0.?, $\ldots$	$[(10, 7)]$
19520.u1	19520q1	19520.u	19520q	$2$	$2$	$ 2^{6} \cdot 5 \cdot 61 $	$ 2^{14} \cdot 5 \cdot 61 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.22	2B	$2440$	$48$	$0$	$1$	$1$		$1$	$6144$	$0.221845$	$436334416/305$	$0.78613$	$2.99599$	$[0, -1, 0, -401, -2959]$	$y^2=x^3-x^2-401x-2959$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 610.6.0.?, 1220.24.0.?, $\ldots$	$[]$
21960.o1	21960e1	21960.o	21960e	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 61 $	$ 2^{8} \cdot 3^{6} \cdot 5 \cdot 61 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$7320$	$48$	$0$	$6.362274649$	$1$		$1$	$9216$	$0.424578$	$436334416/305$	$0.78613$	$3.20405$	$[0, 0, 0, -903, -10438]$	$y^2=x^3-903x-10438$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.1, 610.6.0.?, 1220.24.0.?, $\ldots$	$[(1003/3, 30464/3)]$
24400.bc1	24400f1	24400.bc	24400f	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 61 $	$ 2^{8} \cdot 5^{7} \cdot 61 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$2440$	$48$	$0$	$1$	$4$	$2$	$1$	$18432$	$0.679991$	$436334416/305$	$0.78613$	$3.47402$	$[0, -1, 0, -2508, -47488]$	$y^2=x^3-x^2-2508x-47488$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.3, 488.12.0.?, 610.6.0.?, $\ldots$	$[]$
43920.b1	43920p1	43920.b	43920p	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 61 $	$ 2^{8} \cdot 3^{6} \cdot 5 \cdot 61 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$7320$	$48$	$0$	$1.908860542$	$1$		$5$	$18432$	$0.424578$	$436334416/305$	$0.78613$	$2.99630$	$[0, 0, 0, -903, 10438]$	$y^2=x^3-903x+10438$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.1, 610.6.0.?, 1220.24.0.?, $\ldots$	$[(18, 4)]$
97600.t1	97600bz1	97600.t	97600bz	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 61 $	$ 2^{14} \cdot 5^{7} \cdot 61 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$2440$	$48$	$0$	$1$	$1$		$1$	$147456$	$1.026564$	$436334416/305$	$0.78613$	$3.41682$	$[0, 1, 0, -10033, -389937]$	$y^2=x^3+x^2-10033x-389937$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.2, 488.12.0.?, 610.6.0.?, $\ldots$	$[]$
97600.cg1	97600h1	97600.cg	97600h	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 61 $	$ 2^{14} \cdot 5^{7} \cdot 61 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$2440$	$48$	$0$	$3.558097114$	$1$		$3$	$147456$	$1.026564$	$436334416/305$	$0.78613$	$3.41682$	$[0, -1, 0, -10033, 389937]$	$y^2=x^3-x^2-10033x+389937$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.2, 488.12.0.?, 610.6.0.?, $\ldots$	$[(48, 129)]$
109800.e1	109800by1	109800.e	109800by	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 61 $	$ 2^{8} \cdot 3^{6} \cdot 5^{7} \cdot 61 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$7320$	$48$	$0$	$1$	$1$		$1$	$221184$	$1.229298$	$436334416/305$	$0.78613$	$3.59175$	$[0, 0, 0, -22575, -1304750]$	$y^2=x^3-22575x-1304750$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 610.6.0.?, 1220.24.0.?, $\ldots$	$[]$
119560.b1	119560q1	119560.b	119560q	$2$	$2$	$ 2^{3} \cdot 5 \cdot 7^{2} \cdot 61 $	$ 2^{8} \cdot 5 \cdot 7^{6} \cdot 61 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$17080$	$48$	$0$	$2.030344012$	$1$		$3$	$110592$	$0.848227$	$436334416/305$	$0.78613$	$3.17447$	$[0, 1, 0, -4916, -134240]$	$y^2=x^3+x^2-4916x-134240$	2.3.0.a.1, 4.6.0.b.1, 56.12.0-4.b.1.3, 610.6.0.?, 1220.24.0.?, $\ldots$	$[(86, 294)]$
148840.k1	148840i1	148840.k	148840i	$2$	$2$	$ 2^{3} \cdot 5 \cdot 61^{2} $	$ 2^{8} \cdot 5 \cdot 61^{7} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$2440$	$48$	$0$	$19.16874289$	$1$		$1$	$1428480$	$1.930708$	$436334416/305$	$0.78613$	$4.20669$	$[0, -1, 0, -373340, 87873620]$	$y^2=x^3-x^2-373340x+87873620$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.1, 488.12.0.?, 610.6.0.?, $\ldots$	$[(39982/9, 3542392/9), (19837/6, 1514447/6)]$
175680.dm1	175680b1	175680.dm	175680b	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 61 $	$ 2^{14} \cdot 3^{6} \cdot 5 \cdot 61 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$7320$	$48$	$0$	$1$	$1$		$1$	$147456$	$0.771152$	$436334416/305$	$0.78613$	$2.99672$	$[0, 0, 0, -3612, 83504]$	$y^2=x^3-3612x+83504$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 610.6.0.?, 1220.24.0.?, $\ldots$	$[]$
175680.gg1	175680em1	175680.gg	175680em	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 61 $	$ 2^{14} \cdot 3^{6} \cdot 5 \cdot 61 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$7320$	$48$	$0$	$8.123412825$	$1$		$1$	$147456$	$0.771152$	$436334416/305$	$0.78613$	$2.99672$	$[0, 0, 0, -3612, -83504]$	$y^2=x^3-3612x-83504$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 610.6.0.?, 1220.24.0.?, $\ldots$	$[(11790/7, 1235632/7)]$
219600.fp1	219600fj1	219600.fp	219600fj	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 61 $	$ 2^{8} \cdot 3^{6} \cdot 5^{7} \cdot 61 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$7320$	$48$	$0$	$5.428272896$	$1$		$3$	$442368$	$1.229298$	$436334416/305$	$0.78613$	$3.38934$	$[0, 0, 0, -22575, 1304750]$	$y^2=x^3-22575x+1304750$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 610.6.0.?, 1220.24.0.?, $\ldots$	$[(254, 3458)]$
239120.cp1	239120cp1	239120.cp	239120cp	$2$	$2$	$ 2^{4} \cdot 5 \cdot 7^{2} \cdot 61 $	$ 2^{8} \cdot 5 \cdot 7^{6} \cdot 61 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$17080$	$48$	$0$	$1$	$1$		$1$	$221184$	$0.848227$	$436334416/305$	$0.78613$	$2.99680$	$[0, -1, 0, -4916, 134240]$	$y^2=x^3-x^2-4916x+134240$	2.3.0.a.1, 4.6.0.b.1, 56.12.0-4.b.1.3, 610.6.0.?, 1220.24.0.?, $\ldots$	$[]$
295240.v1	295240v1	295240.v	295240v	$2$	$2$	$ 2^{3} \cdot 5 \cdot 11^{2} \cdot 61 $	$ 2^{8} \cdot 5 \cdot 11^{6} \cdot 61 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$26840$	$48$	$0$	$24.90679550$	$1$		$1$	$537600$	$1.074219$	$436334416/305$	$0.78613$	$3.16195$	$[0, -1, 0, -12140, -510508]$	$y^2=x^3-x^2-12140x-510508$	2.3.0.a.1, 4.6.0.b.1, 88.12.0.?, 610.6.0.?, 1220.24.0.?, $\ldots$	$[(121229726038/12549, 41723671332772720/12549)]$
297680.h1	297680h1	297680.h	297680h	$2$	$2$	$ 2^{4} \cdot 5 \cdot 61^{2} $	$ 2^{8} \cdot 5 \cdot 61^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$2440$	$48$	$0$	$1$	$4$	$2$	$1$	$2856960$	$1.930708$	$436334416/305$	$0.78613$	$3.97534$	$[0, 1, 0, -373340, -87873620]$	$y^2=x^3+x^2-373340x-87873620$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.1, 488.12.0.?, 610.6.0.?, $\ldots$	$[]$
412360.k1	412360k1	412360.k	412360k	$2$	$2$	$ 2^{3} \cdot 5 \cdot 13^{2} \cdot 61 $	$ 2^{8} \cdot 5 \cdot 13^{6} \cdot 61 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$31720$	$48$	$0$	$1$	$4$	$2$	$1$	$884736$	$1.157747$	$436334416/305$	$0.78613$	$3.15776$	$[0, -1, 0, -16956, 854996]$	$y^2=x^3-x^2-16956x+854996$	2.3.0.a.1, 4.6.0.b.1, 104.12.0.?, 610.6.0.?, 1220.24.0.?, $\ldots$	$[]$

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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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