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 (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
13728.c1	13728b2	13728.c	13728b	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{9} \cdot 3^{2} \cdot 11^{3} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1.461663029$	$1$		$5$	$25344$	$0.952753$	$616425416371016/2024451$	$0.95733$	$4.22929$	$[0, -1, 0, -14184, 654948]$	$y^2=x^3-x^2-14184x+654948$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[(72, 42)]$
13728.i1	13728m2	13728.i	13728m	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{9} \cdot 3^{2} \cdot 11^{3} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$25344$	$0.952753$	$616425416371016/2024451$	$0.95733$	$4.22929$	$[0, 1, 0, -14184, -654948]$	$y^2=x^3+x^2-14184x-654948$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
27456.w1	27456i2	27456.w	27456i	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{15} \cdot 3^{2} \cdot 11^{3} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$101376$	$1.299326$	$616425416371016/2024451$	$0.95733$	$4.34938$	$[0, -1, 0, -56737, -5182847]$	$y^2=x^3-x^2-56737x-5182847$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
27456.cl1	27456bh2	27456.cl	27456bh	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11 \cdot 13 $	$ 2^{15} \cdot 3^{2} \cdot 11^{3} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$101376$	$1.299326$	$616425416371016/2024451$	$0.95733$	$4.34938$	$[0, 1, 0, -56737, 5182847]$	$y^2=x^3+x^2-56737x+5182847$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
41184.y1	41184i2	41184.y	41184i	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 11 \cdot 13 $	$ 2^{9} \cdot 3^{8} \cdot 11^{3} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$202752$	$1.502058$	$616425416371016/2024451$	$0.95733$	$4.41237$	$[0, 0, 0, -127659, 17555938]$	$y^2=x^3-127659x+17555938$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
41184.bf1	41184be2	41184.bf	41184be	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 11 \cdot 13 $	$ 2^{9} \cdot 3^{8} \cdot 11^{3} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$202752$	$1.502058$	$616425416371016/2024451$	$0.95733$	$4.41237$	$[0, 0, 0, -127659, -17555938]$	$y^2=x^3-127659x-17555938$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
82368.n1	82368cl2	82368.n	82368cl	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 13 $	$ 2^{15} \cdot 3^{8} \cdot 11^{3} \cdot 13^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$0.653135158$	$1$		$27$	$811008$	$1.848633$	$616425416371016/2024451$	$0.95733$	$4.50959$	$[0, 0, 0, -510636, 140447504]$	$y^2=x^3-510636x+140447504$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[(410, 88), (421, 297)]$
82368.bm1	82368bi2	82368.bm	82368bi	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 13 $	$ 2^{15} \cdot 3^{8} \cdot 11^{3} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$4.857216626$	$1$		$3$	$811008$	$1.848633$	$616425416371016/2024451$	$0.95733$	$4.50959$	$[0, 0, 0, -510636, -140447504]$	$y^2=x^3-510636x-140447504$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[(11054, 1159704)]$
151008.b1	151008l2	151008.b	151008l	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11^{2} \cdot 13 $	$ 2^{9} \cdot 3^{2} \cdot 11^{9} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$3041280$	$2.151699$	$616425416371016/2024451$	$0.95733$	$4.58535$	$[0, -1, 0, -1716304, -864870620]$	$y^2=x^3-x^2-1716304x-864870620$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
151008.bh1	151008bd2	151008.bh	151008bd	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11^{2} \cdot 13 $	$ 2^{9} \cdot 3^{2} \cdot 11^{9} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$3041280$	$2.151699$	$616425416371016/2024451$	$0.95733$	$4.58535$	$[0, 1, 0, -1716304, 864870620]$	$y^2=x^3+x^2-1716304x+864870620$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
178464.x1	178464be2	178464.x	178464be	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 \cdot 13^{2} $	$ 2^{9} \cdot 3^{2} \cdot 11^{3} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1.598312828$	$1$		$7$	$4257792$	$2.235226$	$616425416371016/2024451$	$0.95733$	$4.60489$	$[0, -1, 0, -2397152, 1429332228]$	$y^2=x^3-x^2-2397152x+1429332228$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[(896, 66)]$
178464.cm1	178464by2	178464.cm	178464by	$2$	$2$	$ 2^{5} \cdot 3 \cdot 11 \cdot 13^{2} $	$ 2^{9} \cdot 3^{2} \cdot 11^{3} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$25$	$5$	$1$	$4257792$	$2.235226$	$616425416371016/2024451$	$0.95733$	$4.60489$	$[0, 1, 0, -2397152, -1429332228]$	$y^2=x^3+x^2-2397152x-1429332228$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
302016.dn1	302016dn2	302016.dn	302016dn	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11^{2} \cdot 13 $	$ 2^{15} \cdot 3^{2} \cdot 11^{9} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$12165120$	$2.498276$	$616425416371016/2024451$	$0.95733$	$4.66306$	$[0, -1, 0, -6865217, 6925830177]$	$y^2=x^3-x^2-6865217x+6925830177$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
302016.gu1	302016gu2	302016.gu	302016gu	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11^{2} \cdot 13 $	$ 2^{15} \cdot 3^{2} \cdot 11^{9} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$12.09192653$	$1$		$1$	$12165120$	$2.498276$	$616425416371016/2024451$	$0.95733$	$4.66306$	$[0, 1, 0, -6865217, -6925830177]$	$y^2=x^3+x^2-6865217x-6925830177$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[(2114499/25, 1447605432/25)]$
343200.ci1	343200ci2	343200.ci	343200ci	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 $	$ 2^{9} \cdot 3^{2} \cdot 5^{6} \cdot 11^{3} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$7.791874405$	$1$		$1$	$3244032$	$1.757471$	$616425416371016/2024451$	$0.95733$	$3.91885$	$[0, -1, 0, -354608, -81159288]$	$y^2=x^3-x^2-354608x-81159288$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[(9013/3, 642950/3)]$
343200.co1	343200co2	343200.co	343200co	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 $	$ 2^{9} \cdot 3^{2} \cdot 5^{6} \cdot 11^{3} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$3244032$	$1.757471$	$616425416371016/2024451$	$0.95733$	$3.91885$	$[0, 1, 0, -354608, 81159288]$	$y^2=x^3+x^2-354608x+81159288$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
356928.bg1	356928bg2	356928.bg	356928bg	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11 \cdot 13^{2} $	$ 2^{15} \cdot 3^{2} \cdot 11^{3} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$17031168$	$2.581802$	$616425416371016/2024451$	$0.95733$	$4.68052$	$[0, -1, 0, -9588609, -11425069215]$	$y^2=x^3-x^2-9588609x-11425069215$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
356928.es1	356928es2	356928.es	356928es	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11 \cdot 13^{2} $	$ 2^{15} \cdot 3^{2} \cdot 11^{3} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$17031168$	$2.581802$	$616425416371016/2024451$	$0.95733$	$4.68052$	$[0, 1, 0, -9588609, 11425069215]$	$y^2=x^3+x^2-9588609x+11425069215$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
453024.cs1	453024cs2	453024.cs	453024cs	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 11^{2} \cdot 13 $	$ 2^{9} \cdot 3^{8} \cdot 11^{9} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1$	$1$		$1$	$24330240$	$2.701008$	$616425416371016/2024451$	$0.95733$	$4.70468$	$[0, 0, 0, -15446739, 23366953478]$	$y^2=x^3-15446739x+23366953478$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[ ]$
453024.dv1	453024dv2	453024.dv	453024dv	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 11^{2} \cdot 13 $	$ 2^{9} \cdot 3^{8} \cdot 11^{9} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$21.88349657$	$1$		$1$	$24330240$	$2.701008$	$616425416371016/2024451$	$0.95733$	$4.70468$	$[0, 0, 0, -15446739, -23366953478]$	$y^2=x^3-15446739x-23366953478$	2.3.0.a.1, 88.6.0.?, 156.6.0.?, 3432.12.0.?	$[(741410387729/12598, 160189376873912001/12598)]$

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Elliptic 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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