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 (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
11424.g4	11424a4	11424.g	11424a	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{12} \cdot 3^{3} \cdot 7 \cdot 17^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$6.057254069$	$1$		$1$	$10752$	$0.758275$	$6518244032/15785469$	$0.91054$	$3.43277$	$[0, -1, 0, 623, 10465]$	$y^2=x^3-x^2+623x+10465$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 28.12.0-4.c.1.1, 84.24.0.?, $\ldots$	$[(-261/5, 6512/5)]$
11424.v4	11424v4	11424.v	11424v	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{12} \cdot 3^{3} \cdot 7 \cdot 17^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$10752$	$0.758275$	$6518244032/15785469$	$0.91054$	$3.43277$	$[0, 1, 0, 623, -10465]$	$y^2=x^3+x^2+623x-10465$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 28.12.0-4.c.1.2, 84.24.0.?, $\ldots$	$[ ]$
22848.m4	22848m1	22848.m	22848m	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{6} \cdot 3^{3} \cdot 7 \cdot 17^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$1$	$4$	$2$	$1$	$10752$	$0.411701$	$6518244032/15785469$	$0.91054$	$2.78133$	$[0, -1, 0, 156, -1386]$	$y^2=x^3-x^2+156x-1386$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 56.12.0-4.c.1.1, 84.12.0.?, $\ldots$	$[ ]$
22848.bq4	22848w1	22848.bq	22848w	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17 $	$ - 2^{6} \cdot 3^{3} \cdot 7 \cdot 17^{4} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$4.807066069$	$1$		$5$	$10752$	$0.411701$	$6518244032/15785469$	$0.91054$	$2.78133$	$[0, 1, 0, 156, 1386]$	$y^2=x^3+x^2+156x+1386$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 56.12.0-4.c.1.2, 84.12.0.?, $\ldots$	$[(-3, 30), (9, 60)]$
34272.f4	34272bh2	34272.f	34272bh	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 17 $	$ - 2^{12} \cdot 3^{9} \cdot 7 \cdot 17^{4} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$2856$	$48$	$0$	$1$	$1$		$3$	$86016$	$1.307581$	$6518244032/15785469$	$0.91054$	$3.70287$	$[0, 0, 0, 5604, -288160]$	$y^2=x^3+5604x-288160$	2.3.0.a.1, 4.12.0-4.c.1.1, 84.24.0.?, 408.24.0.?, 952.24.0.?, $\ldots$	$[ ]$
34272.n4	34272u2	34272.n	34272u	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 17 $	$ - 2^{12} \cdot 3^{9} \cdot 7 \cdot 17^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$86016$	$1.307581$	$6518244032/15785469$	$0.91054$	$3.70287$	$[0, 0, 0, 5604, 288160]$	$y^2=x^3+5604x+288160$	2.3.0.a.1, 4.12.0-4.c.1.2, 84.24.0.?, 408.24.0.?, 952.24.0.?, $\ldots$	$[ ]$
68544.dv4	68544bn1	68544.dv	68544bn	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 17 $	$ - 2^{6} \cdot 3^{9} \cdot 7 \cdot 17^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$2856$	$48$	$0$	$8.459146387$	$1$		$1$	$86016$	$0.961007$	$6518244032/15785469$	$0.91054$	$3.09889$	$[0, 0, 0, 1401, -36020]$	$y^2=x^3+1401x-36020$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 84.12.0.?, 168.24.0.?, $\ldots$	$[(11801/10, 1331451/10)]$
68544.dz4	68544cn1	68544.dz	68544cn	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 17 $	$ - 2^{6} \cdot 3^{9} \cdot 7 \cdot 17^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$86016$	$0.961007$	$6518244032/15785469$	$0.91054$	$3.09889$	$[0, 0, 0, 1401, 36020]$	$y^2=x^3+1401x+36020$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 84.12.0.?, 168.24.0.?, $\ldots$	$[ ]$
79968.f4	79968bx2	79968.f	79968bx	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{3} \cdot 7^{7} \cdot 17^{4} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$2856$	$48$	$0$	$1$	$1$		$3$	$516096$	$1.731230$	$6518244032/15785469$	$0.91054$	$3.87528$	$[0, -1, 0, 30511, 3650529]$	$y^2=x^3-x^2+30511x+3650529$	2.3.0.a.1, 4.12.0-4.c.1.1, 84.24.0.?, 408.24.0.?, 952.24.0.?, $\ldots$	$[ ]$
79968.bv4	79968be2	79968.bv	79968be	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{3} \cdot 7^{7} \cdot 17^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$516096$	$1.731230$	$6518244032/15785469$	$0.91054$	$3.87528$	$[0, 1, 0, 30511, -3650529]$	$y^2=x^3+x^2+30511x-3650529$	2.3.0.a.1, 4.12.0-4.c.1.2, 84.24.0.?, 408.24.0.?, 952.24.0.?, $\ldots$	$[ ]$
159936.dw4	159936jy1	159936.dw	159936jy	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{3} \cdot 7^{7} \cdot 17^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$2856$	$48$	$0$	$10.79487937$	$1$		$1$	$516096$	$1.384657$	$6518244032/15785469$	$0.91054$	$3.30403$	$[0, -1, 0, 7628, -460130]$	$y^2=x^3-x^2+7628x-460130$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 84.12.0.?, 168.24.0.?, $\ldots$	$[(30483/17, 6030830/17)]$
159936.ju4	159936hk1	159936.ju	159936hk	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{3} \cdot 7^{7} \cdot 17^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$516096$	$1.384657$	$6518244032/15785469$	$0.91054$	$3.30403$	$[0, 1, 0, 7628, 460130]$	$y^2=x^3+x^2+7628x+460130$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 84.12.0.?, 168.24.0.?, $\ldots$	$[ ]$
194208.f4	194208w3	194208.f	194208w	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17^{2} $	$ - 2^{12} \cdot 3^{3} \cdot 7 \cdot 17^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$3096576$	$2.174881$	$6518244032/15785469$	$0.91054$	$4.03010$	$[0, -1, 0, 179951, -52494431]$	$y^2=x^3-x^2+179951x-52494431$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 84.12.0.?, 168.24.0.?, $\ldots$	$[ ]$
194208.bq4	194208bk3	194208.bq	194208bk	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 17^{2} $	$ - 2^{12} \cdot 3^{3} \cdot 7 \cdot 17^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$2856$	$48$	$0$	$7.344972003$	$1$		$3$	$3096576$	$2.174881$	$6518244032/15785469$	$0.91054$	$4.03010$	$[0, 1, 0, 179951, 52494431]$	$y^2=x^3+x^2+179951x+52494431$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 84.12.0.?, 168.24.0.?, $\ldots$	$[(6173, 486240)]$
239904.cw4	239904cw3	239904.cw	239904cw	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{9} \cdot 7^{7} \cdot 17^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$1$	$1$		$1$	$4128768$	$2.280537$	$6518244032/15785469$	$0.91054$	$4.06370$	$[0, 0, 0, 274596, 98838880]$	$y^2=x^3+274596x+98838880$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 28.12.0-4.c.1.2, 84.24.0.?, $\ldots$	$[ ]$
239904.di4	239904di3	239904.di	239904di	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{12} \cdot 3^{9} \cdot 7^{7} \cdot 17^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$4.745358379$	$1$		$3$	$4128768$	$2.280537$	$6518244032/15785469$	$0.91054$	$4.06370$	$[0, 0, 0, 274596, -98838880]$	$y^2=x^3+274596x-98838880$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 28.12.0-4.c.1.1, 84.24.0.?, $\ldots$	$[(152005, 59263785)]$
285600.g4	285600g3	285600.g	285600g	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ - 2^{12} \cdot 3^{3} \cdot 5^{6} \cdot 7 \cdot 17^{4} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$14280$	$48$	$0$	$5.393885793$	$1$		$11$	$1376256$	$1.562994$	$6518244032/15785469$	$0.91054$	$3.32188$	$[0, -1, 0, 15567, -1339263]$	$y^2=x^3-x^2+15567x-1339263$	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.1, 84.12.0.?, 140.12.0.?, $\ldots$	$[(407, 8500), (832, 24225)]$
285600.ge4	285600ge3	285600.ge	285600ge	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ - 2^{12} \cdot 3^{3} \cdot 5^{6} \cdot 7 \cdot 17^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$14280$	$48$	$0$	$0.755288475$	$1$		$9$	$1376256$	$1.562994$	$6518244032/15785469$	$0.91054$	$3.32188$	$[0, 1, 0, 15567, 1339263]$	$y^2=x^3+x^2+15567x+1339263$	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.2, 84.12.0.?, 140.12.0.?, $\ldots$	$[(18, 1275)]$
388416.dp4	388416dp1	388416.dp	388416dp	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17^{2} $	$ - 2^{6} \cdot 3^{3} \cdot 7 \cdot 17^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$2856$	$48$	$0$	$1$	$16$	$2$	$1$	$3096576$	$1.828308$	$6518244032/15785469$	$0.91054$	$3.48990$	$[0, -1, 0, 44988, 6539310]$	$y^2=x^3-x^2+44988x+6539310$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 168.24.0.?, $\ldots$	$[ ]$
388416.hg4	388416hg1	388416.hg	388416hg	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 17^{2} $	$ - 2^{6} \cdot 3^{3} \cdot 7 \cdot 17^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$2856$	$48$	$0$	$1$	$4$	$2$	$1$	$3096576$	$1.828308$	$6518244032/15785469$	$0.91054$	$3.48990$	$[0, 1, 0, 44988, -6539310]$	$y^2=x^3+x^2+44988x-6539310$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 168.24.0.?, $\ldots$	$[ ]$
479808.dh4	479808dh1	479808.dh	479808dh	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{9} \cdot 7^{7} \cdot 17^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$4.584085399$	$1$		$3$	$4128768$	$1.933962$	$6518244032/15785469$	$0.91054$	$3.53045$	$[0, 0, 0, 68649, -12354860]$	$y^2=x^3+68649x-12354860$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 56.12.0-4.c.1.2, 84.12.0.?, $\ldots$	$[(1904, 83790)]$
479808.ew4	479808ew1	479808.ew	479808ew	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{9} \cdot 7^{7} \cdot 17^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2856$	$48$	$0$	$9.223924876$	$1$		$1$	$4128768$	$1.933962$	$6518244032/15785469$	$0.91054$	$3.53045$	$[0, 0, 0, 68649, 12354860]$	$y^2=x^3+68649x+12354860$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 56.12.0-4.c.1.1, 84.12.0.?, $\ldots$	$[(69496/3, 18331390/3)]$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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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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