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
24480.b2	24480v1	24480.b	24480v	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 17 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$36864$	$0.892134$	$-11852352/265625$	$0.99754$	$3.36609$	$[0, 0, 0, -513, -28188]$	$y^2=x^3-513x-28188$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[ ]$
24480.n2	24480a1	24480.n	24480a	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 17 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$3.520019607$	$1$		$3$	$36864$	$0.892134$	$-11852352/265625$	$0.99754$	$3.36609$	$[0, 0, 0, -513, 28188]$	$y^2=x^3-513x+28188$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[(13, 154)]$
24480.q2	24480f1	24480.q	24480f	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 17 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$0.524736278$	$1$		$7$	$12288$	$0.342828$	$-11852352/265625$	$0.99754$	$2.71382$	$[0, 0, 0, -57, 1044]$	$y^2=x^3-57x+1044$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[(3, 30)]$
24480.bi2	24480ba1	24480.bi	24480ba	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 17 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$12288$	$0.342828$	$-11852352/265625$	$0.99754$	$2.71382$	$[0, 0, 0, -57, -1044]$	$y^2=x^3-57x-1044$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[ ]$
48960.i2	48960o2	48960.i	48960o	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 17 $	$ - 2^{12} \cdot 3^{3} \cdot 5^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$49152$	$0.689402$	$-11852352/265625$	$0.99754$	$2.92475$	$[0, 0, 0, -228, 8352]$	$y^2=x^3-228x+8352$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[ ]$
48960.cx2	48960m2	48960.cx	48960m	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 17 $	$ - 2^{12} \cdot 3^{3} \cdot 5^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$49152$	$0.689402$	$-11852352/265625$	$0.99754$	$2.92475$	$[0, 0, 0, -228, -8352]$	$y^2=x^3-228x-8352$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[ ]$
48960.dk2	48960t2	48960.dk	48960t	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 17 $	$ - 2^{12} \cdot 3^{9} \cdot 5^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$147456$	$1.238707$	$-11852352/265625$	$0.99754$	$3.53516$	$[0, 0, 0, -2052, -225504]$	$y^2=x^3-2052x-225504$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[ ]$
48960.fv2	48960r2	48960.fv	48960r	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 17 $	$ - 2^{12} \cdot 3^{9} \cdot 5^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$147456$	$1.238707$	$-11852352/265625$	$0.99754$	$3.53516$	$[0, 0, 0, -2052, 225504]$	$y^2=x^3-2052x+225504$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[ ]$
122400.e2	122400cj1	122400.e	122400cj	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{12} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$2.865852695$	$1$		$3$	$884736$	$1.696854$	$-11852352/265625$	$0.99754$	$3.72795$	$[0, 0, 0, -12825, 3523500]$	$y^2=x^3-12825x+3523500$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[(360, 6750)]$
122400.i2	122400c1	122400.i	122400c	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{12} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$5.028258957$	$1$		$3$	$294912$	$1.147547$	$-11852352/265625$	$0.99754$	$3.16528$	$[0, 0, 0, -1425, -130500]$	$y^2=x^3-1425x-130500$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[(181, 2354)]$
122400.ea2	122400cf1	122400.ea	122400cf	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{12} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$294912$	$1.147547$	$-11852352/265625$	$0.99754$	$3.16528$	$[0, 0, 0, -1425, 130500]$	$y^2=x^3-1425x+130500$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[ ]$
122400.ee2	122400i1	122400.ee	122400i	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{12} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$4$	$2$	$1$	$884736$	$1.696854$	$-11852352/265625$	$0.99754$	$3.72795$	$[0, 0, 0, -12825, -3523500]$	$y^2=x^3-12825x-3523500$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[ ]$
244800.s2	244800s2	244800.s	244800s	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{3} \cdot 5^{12} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$3.211478951$	$1$		$3$	$1179648$	$1.494120$	$-11852352/265625$	$0.99754$	$3.32363$	$[0, 0, 0, -5700, -1044000]$	$y^2=x^3-5700x-1044000$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[(360, 6600)]$
244800.bw2	244800bw2	244800.bw	244800bw	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{9} \cdot 5^{12} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$3538944$	$2.043427$	$-11852352/265625$	$0.99754$	$3.85487$	$[0, 0, 0, -51300, 28188000]$	$y^2=x^3-51300x+28188000$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[ ]$
244800.rm2	244800rm2	244800.rm	244800rm	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{9} \cdot 5^{12} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$9$	$3$	$1$	$3538944$	$2.043427$	$-11852352/265625$	$0.99754$	$3.85487$	$[0, 0, 0, -51300, -28188000]$	$y^2=x^3-51300x-28188000$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[ ]$
244800.sn2	244800sn2	244800.sn	244800sn	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{3} \cdot 5^{12} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$6.515281562$	$1$		$3$	$1179648$	$1.494120$	$-11852352/265625$	$0.99754$	$3.32363$	$[0, 0, 0, -5700, 1044000]$	$y^2=x^3-5700x+1044000$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[(11640, 1255800)]$
416160.f2	416160f1	416160.f	416160f	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 17^{2} $	$ - 2^{6} \cdot 3^{3} \cdot 5^{6} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$3538944$	$1.759434$	$-11852352/265625$	$0.99754$	$3.43339$	$[0, 0, 0, -16473, -5129172]$	$y^2=x^3-16473x-5129172$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[ ]$
416160.by2	416160by1	416160.by	416160by	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 17^{2} $	$ - 2^{6} \cdot 3^{3} \cdot 5^{6} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$7.134947467$	$1$		$1$	$3538944$	$1.759434$	$-11852352/265625$	$0.99754$	$3.43339$	$[0, 0, 0, -16473, 5129172]$	$y^2=x^3-16473x+5129172$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[(24973/7, 3897454/7)]$
416160.cl2	416160cl1	416160.cl	416160cl	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 17^{2} $	$ - 2^{6} \cdot 3^{9} \cdot 5^{6} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$10616832$	$2.308739$	$-11852352/265625$	$0.99754$	$3.94284$	$[0, 0, 0, -148257, 138487644]$	$y^2=x^3-148257x+138487644$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[ ]$
416160.dr2	416160dr1	416160.dr	416160dr	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 17^{2} $	$ - 2^{6} \cdot 3^{9} \cdot 5^{6} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$4.239741605$	$1$		$1$	$10616832$	$2.308739$	$-11852352/265625$	$0.99754$	$3.94284$	$[0, 0, 0, -148257, -138487644]$	$y^2=x^3-148257x-138487644$	2.3.0.a.1, 60.6.0.b.1, 102.6.0.?, 340.6.0.?, 1020.12.0.?	$[(9673/3, 829430/3)]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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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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