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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
10920.o2	10920q2	10920.o	10920q	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{11} \cdot 3^{8} \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$18432$	$0.919789$	$-166792350818/194041575$	$0.89225$	$3.71751$	$[0, 1, 0, -1456, -37600]$	$y^2=x^3+x^2-1456x-37600$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
21840.n2	21840e2	21840.n	21840e	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{11} \cdot 3^{8} \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1.045011357$	$1$		$7$	$36864$	$0.919789$	$-166792350818/194041575$	$0.89225$	$3.45961$	$[0, -1, 0, -1456, 37600]$	$y^2=x^3-x^2-1456x+37600$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[(18, 130)]$
32760.v2	32760t2	32760.v	32760t	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{11} \cdot 3^{14} \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$147456$	$1.469095$	$-166792350818/194041575$	$0.89225$	$3.95869$	$[0, 0, 0, -13107, 1002094]$	$y^2=x^3-13107x+1002094$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
54600.bg2	54600h2	54600.bg	54600h	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 $	$ - 2^{11} \cdot 3^{8} \cdot 5^{8} \cdot 7 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$4$	$2$	$1$	$442368$	$1.724508$	$-166792350818/194041575$	$0.89225$	$4.05429$	$[0, -1, 0, -36408, -4627188]$	$y^2=x^3-x^2-36408x-4627188$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
65520.eo2	65520br2	65520.eo	65520br	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{11} \cdot 3^{14} \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$2.332679474$	$1$		$5$	$294912$	$1.469095$	$-166792350818/194041575$	$0.89225$	$3.71127$	$[0, 0, 0, -13107, -1002094]$	$y^2=x^3-13107x-1002094$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[(157, 900)]$
76440.bm2	76440cf2	76440.bm	76440cf	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 $	$ - 2^{11} \cdot 3^{8} \cdot 5^{2} \cdot 7^{7} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$884736$	$1.892744$	$-166792350818/194041575$	$0.89225$	$4.11251$	$[0, -1, 0, -71360, 12754092]$	$y^2=x^3-x^2-71360x+12754092$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
87360.bt2	87360w2	87360.bt	87360w	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{17} \cdot 3^{8} \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$4.450096337$	$1$		$17$	$294912$	$1.266363$	$-166792350818/194041575$	$0.89225$	$3.40361$	$[0, -1, 0, -5825, -294975]$	$y^2=x^3-x^2-5825x-294975$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[(225, 3120), (97, 208)]$
87360.hk2	87360hd2	87360.hk	87360hd	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{17} \cdot 3^{8} \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$0.548199078$	$1$		$9$	$294912$	$1.266363$	$-166792350818/194041575$	$0.89225$	$3.40361$	$[0, 1, 0, -5825, 294975]$	$y^2=x^3+x^2-5825x+294975$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[(-17, 624)]$
109200.dx2	109200bo2	109200.dx	109200bo	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 $	$ - 2^{11} \cdot 3^{8} \cdot 5^{8} \cdot 7 \cdot 13^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$0.528489122$	$1$		$31$	$884736$	$1.724508$	$-166792350818/194041575$	$0.89225$	$3.81205$	$[0, 1, 0, -36408, 4627188]$	$y^2=x^3+x^2-36408x+4627188$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[(-12, 2250), (738, 19500)]$
141960.ch2	141960be2	141960.ch	141960be	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} $	$ - 2^{11} \cdot 3^{8} \cdot 5^{2} \cdot 7 \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$3096576$	$2.202263$	$-166792350818/194041575$	$0.89225$	$4.21100$	$[0, 1, 0, -246120, -81622800]$	$y^2=x^3+x^2-246120x-81622800$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
152880.ga2	152880fm2	152880.ga	152880fm	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 $	$ - 2^{11} \cdot 3^{8} \cdot 5^{2} \cdot 7^{7} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$1769472$	$1.892744$	$-166792350818/194041575$	$0.89225$	$3.87372$	$[0, 1, 0, -71360, -12754092]$	$y^2=x^3+x^2-71360x-12754092$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
163800.cw2	163800t2	163800.cw	163800t	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 $	$ - 2^{11} \cdot 3^{14} \cdot 5^{8} \cdot 7 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$3538944$	$2.273815$	$-166792350818/194041575$	$0.89225$	$4.23232$	$[0, 0, 0, -327675, 125261750]$	$y^2=x^3-327675x+125261750$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
229320.a2	229320dp2	229320.a	229320dp	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 $	$ - 2^{11} \cdot 3^{14} \cdot 5^{2} \cdot 7^{7} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$3.234835351$	$1$		$3$	$7077888$	$2.442051$	$-166792350818/194041575$	$0.89225$	$4.28051$	$[0, 0, 0, -642243, -343718242]$	$y^2=x^3-642243x-343718242$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[(1414, 39690)]$
262080.dk2	262080dk2	262080.dk	262080dk	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{17} \cdot 3^{14} \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$2359296$	$1.815668$	$-166792350818/194041575$	$0.89225$	$3.63223$	$[0, 0, 0, -52428, 8016752]$	$y^2=x^3-52428x+8016752$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
262080.ds2	262080ds2	262080.ds	262080ds	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{17} \cdot 3^{14} \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$2359296$	$1.815668$	$-166792350818/194041575$	$0.89225$	$3.63223$	$[0, 0, 0, -52428, -8016752]$	$y^2=x^3-52428x-8016752$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
283920.cw2	283920cw2	283920.cw	283920cw	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} $	$ - 2^{11} \cdot 3^{8} \cdot 5^{2} \cdot 7 \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$6193152$	$2.202263$	$-166792350818/194041575$	$0.89225$	$3.97854$	$[0, -1, 0, -246120, 81622800]$	$y^2=x^3-x^2-246120x+81622800$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
327600.gi2	327600gi2	327600.gi	327600gi	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 $	$ - 2^{11} \cdot 3^{14} \cdot 5^{8} \cdot 7 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$7077888$	$2.273815$	$-166792350818/194041575$	$0.89225$	$4.00132$	$[0, 0, 0, -327675, -125261750]$	$y^2=x^3-327675x-125261750$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
382200.jp2	382200jp2	382200.jp	382200jp	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$ - 2^{11} \cdot 3^{8} \cdot 5^{8} \cdot 7^{7} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$21233664$	$2.697464$	$-166792350818/194041575$	$0.89225$	$4.34885$	$[0, 1, 0, -1784008, 1590693488]$	$y^2=x^3+x^2-1784008x+1590693488$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
425880.cs2	425880cs2	425880.cs	425880cs	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13^{2} $	$ - 2^{11} \cdot 3^{14} \cdot 5^{2} \cdot 7 \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$24772608$	$2.751572$	$-166792350818/194041575$	$0.89225$	$4.36263$	$[0, 0, 0, -2215083, 2201600518]$	$y^2=x^3-2215083x+2201600518$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
436800.fn2	436800fn2	436800.fn	436800fn	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 $	$ - 2^{17} \cdot 3^{8} \cdot 5^{8} \cdot 7 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$3.470431504$	$1$		$5$	$7077888$	$2.071083$	$-166792350818/194041575$	$0.89225$	$3.72537$	$[0, -1, 0, -145633, 37163137]$	$y^2=x^3-x^2-145633x+37163137$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[(-149, 7452)]$
436800.pj2	436800pj2	436800.pj	436800pj	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 $	$ - 2^{17} \cdot 3^{8} \cdot 5^{8} \cdot 7 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$7077888$	$2.071083$	$-166792350818/194041575$	$0.89225$	$3.72537$	$[0, 1, 0, -145633, -37163137]$	$y^2=x^3+x^2-145633x-37163137$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[]$
458640.hf2	458640hf2	458640.hf	458640hf	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 $	$ - 2^{11} \cdot 3^{14} \cdot 5^{2} \cdot 7^{7} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1.586929892$	$1$		$7$	$14155776$	$2.442051$	$-166792350818/194041575$	$0.89225$	$4.05291$	$[0, 0, 0, -642243, 343718242]$	$y^2=x^3-642243x+343718242$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[(917, 22932)]$

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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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