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
9240.bd3	9240bg4	9240.bd	9240bg	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3 \cdot 5^{12} \cdot 7^{3} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1.843172719$	$1$		$3$	$184320$	$2.293793$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.67290$	$[0, 1, 0, -608256, 204877200]$	$y^2=x^3+x^2-608256x+204877200$	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.?, $\ldots$	$[(176, 10164)]$
18480.e3	18480c4	18480.e	18480c	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3 \cdot 5^{12} \cdot 7^{3} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$23.44799965$	$1$		$1$	$368640$	$2.293793$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.27266$	$[0, -1, 0, -608256, -204877200]$	$y^2=x^3-x^2-608256x-204877200$	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.?, $\ldots$	$[(167752443749/226, 68707351030219627/226)]$
27720.bn3	27720v3	27720.bn	27720v	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{7} \cdot 5^{12} \cdot 7^{3} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$1474560$	$2.843098$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.70803$	$[0, 0, 0, -5474307, -5537158706]$	$y^2=x^3-5474307x-5537158706$	2.3.0.a.1, 4.12.0-4.c.1.2, 84.24.0.?, 1320.24.0.?, 3080.24.0.?, $\ldots$	$[]$
46200.i3	46200f3	46200.i	46200f	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3 \cdot 5^{18} \cdot 7^{3} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$4423680$	$3.098511$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.72192$	$[0, -1, 0, -15206408, 25640062812]$	$y^2=x^3-x^2-15206408x+25640062812$	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.1, 84.12.0.?, 88.12.0.?, $\ldots$	$[]$
55440.du3	55440bi3	55440.du	55440bi	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{7} \cdot 5^{12} \cdot 7^{3} \cdot 11^{4} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$9240$	$48$	$0$	$1$	$1$		$3$	$2949120$	$2.843098$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.34582$	$[0, 0, 0, -5474307, 5537158706]$	$y^2=x^3-5474307x+5537158706$	2.3.0.a.1, 4.12.0-4.c.1.1, 84.24.0.?, 1320.24.0.?, 3080.24.0.?, $\ldots$	$[]$
64680.bc3	64680ch3	64680.bc	64680ch	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3 \cdot 5^{12} \cdot 7^{9} \cdot 11^{4} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$9240$	$48$	$0$	$6.701205057$	$1$		$5$	$8847360$	$3.266747$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.73036$	$[0, -1, 0, -29804560, -70332488708]$	$y^2=x^3-x^2-29804560x-70332488708$	2.3.0.a.1, 4.12.0-4.c.1.1, 84.24.0.?, 1320.24.0.?, 3080.24.0.?, $\ldots$	$[(30414, 5211100)]$
73920.dg3	73920br3	73920.dg	73920br	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{16} \cdot 3 \cdot 5^{12} \cdot 7^{3} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$0.841290864$	$1$		$7$	$2949120$	$2.640366$	$-24304331176056594436/3678122314453125$	$1.07918$	$4.99163$	$[0, -1, 0, -2433025, 1641450625]$	$y^2=x^3-x^2-2433025x+1641450625$	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.?, $\ldots$	$[(675, 17500)]$
73920.gy3	73920hv3	73920.gy	73920hv	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{16} \cdot 3 \cdot 5^{12} \cdot 7^{3} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$2.734788239$	$1$		$3$	$2949120$	$2.640366$	$-24304331176056594436/3678122314453125$	$1.07918$	$4.99163$	$[0, 1, 0, -2433025, -1641450625]$	$y^2=x^3+x^2-2433025x-1641450625$	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.?, $\ldots$	$[(6775, 541200)]$
92400.gq3	92400cl3	92400.gq	92400cl	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3 \cdot 5^{18} \cdot 7^{3} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$17.01192207$	$1$		$1$	$8847360$	$3.098511$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.37504$	$[0, 1, 0, -15206408, -25640062812]$	$y^2=x^3+x^2-15206408x-25640062812$	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.2, 84.12.0.?, 88.12.0.?, $\ldots$	$[(980810271/37, 30716474120178/37)]$
101640.bm3	101640w3	101640.bm	101640w	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3 \cdot 5^{12} \cdot 7^{3} \cdot 11^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$64.03422221$	$1$		$1$	$22118400$	$3.492741$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.74093$	$[0, 1, 0, -73599016, -272985949216]$	$y^2=x^3+x^2-73599016x-272985949216$	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.5, 84.12.0.?, 132.12.0.?, $\ldots$	$[(682711468829992169560788472051/4942727315053, 533150331657963638677234286614133695173656250/4942727315053)]$
129360.fw3	129360cv3	129360.fw	129360cv	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3 \cdot 5^{12} \cdot 7^{9} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$17694720$	$3.266747$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.39291$	$[0, 1, 0, -29804560, 70332488708]$	$y^2=x^3+x^2-29804560x+70332488708$	2.3.0.a.1, 4.12.0-4.c.1.2, 84.24.0.?, 1320.24.0.?, 3080.24.0.?, $\ldots$	$[]$
138600.a3	138600bw3	138600.a	138600bw	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{7} \cdot 5^{18} \cdot 7^{3} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$13.09491880$	$1$		$1$	$35389440$	$3.647816$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.74772$	$[0, 0, 0, -136857675, -692144838250]$	$y^2=x^3-136857675x-692144838250$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 84.12.0.?, 264.12.0.?, $\ldots$	$[(11473259/23, 31119456148/23)]$
194040.b3	194040dy4	194040.b	194040dy	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3^{7} \cdot 5^{12} \cdot 7^{9} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$3.611710957$	$1$		$3$	$70778880$	$3.816055$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.75469$	$[0, 0, 0, -268241043, 1899245436158]$	$y^2=x^3-268241043x+1899245436158$	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.?, $\ldots$	$[(9583, 456876)]$
203280.bh3	203280gq4	203280.bh	203280gq	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3 \cdot 5^{12} \cdot 7^{3} \cdot 11^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$6.296905531$	$1$		$1$	$44236800$	$3.492741$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.41536$	$[0, -1, 0, -73599016, 272985949216]$	$y^2=x^3-x^2-73599016x+272985949216$	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.5, 84.12.0.?, 132.12.0.?, $\ldots$	$[(230001/4, 94609375/4)]$
221760.c3	221760fe4	221760.c	221760fe	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{16} \cdot 3^{7} \cdot 5^{12} \cdot 7^{3} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$9240$	$48$	$0$	$5.101918037$	$1$		$3$	$23592960$	$3.189671$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.08163$	$[0, 0, 0, -21897228, 44297269648]$	$y^2=x^3-21897228x+44297269648$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 84.12.0.?, 168.24.0.?, $\ldots$	$[(2268, 79376)]$
221760.ez3	221760kg3	221760.ez	221760kg	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{16} \cdot 3^{7} \cdot 5^{12} \cdot 7^{3} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$23592960$	$3.189671$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.08163$	$[0, 0, 0, -21897228, -44297269648]$	$y^2=x^3-21897228x-44297269648$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 84.12.0.?, 168.24.0.?, $\ldots$	$[]$
277200.kx3	277200kx4	277200.kx	277200kx	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{7} \cdot 5^{18} \cdot 7^{3} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$70778880$	$3.647816$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.42983$	$[0, 0, 0, -136857675, 692144838250]$	$y^2=x^3-136857675x+692144838250$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 84.12.0.?, 264.12.0.?, $\ldots$	$[]$
304920.ct3	304920ct4	304920.ct	304920ct	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{7} \cdot 5^{12} \cdot 7^{3} \cdot 11^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$3.621051645$	$1$		$3$	$176947200$	$4.042046$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.76347$	$[0, 0, 0, -662391147, 7369958237686]$	$y^2=x^3-662391147x+7369958237686$	2.3.0.a.1, 4.6.0.c.1, 44.12.0-4.c.1.1, 84.12.0.?, 120.12.0.?, $\ldots$	$[(20507, 1552500)]$
323400.js3	323400js3	323400.js	323400js	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3 \cdot 5^{18} \cdot 7^{9} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$25$	$5$	$1$	$212336640$	$4.071465$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.76457$	$[0, 1, 0, -745114008, -8793051316512]$	$y^2=x^3+x^2-745114008x-8793051316512$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 84.12.0.?, 264.12.0.?, $\ldots$	$[]$
369600.lq3	369600lq3	369600.lq	369600lq	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{16} \cdot 3 \cdot 5^{18} \cdot 7^{3} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$70778880$	$3.445084$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.11822$	$[0, -1, 0, -60825633, -205059676863]$	$y^2=x^3-x^2-60825633x-205059676863$	2.3.0.a.1, 4.6.0.c.1, 84.12.0.?, 88.12.0.?, 120.12.0.?, $\ldots$	$[]$
369600.oe3	369600oe4	369600.oe	369600oe	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{16} \cdot 3 \cdot 5^{18} \cdot 7^{3} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$16$	$2$	$1$	$70778880$	$3.445084$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.11822$	$[0, 1, 0, -60825633, 205059676863]$	$y^2=x^3+x^2-60825633x+205059676863$	2.3.0.a.1, 4.6.0.c.1, 84.12.0.?, 88.12.0.?, 120.12.0.?, $\ldots$	$[]$
388080.ef3	388080ef3	388080.ef	388080ef	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3^{7} \cdot 5^{12} \cdot 7^{9} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$141557760$	$3.816055$	$-24304331176056594436/3678122314453125$	$1.07918$	$5.44473$	$[0, 0, 0, -268241043, -1899245436158]$	$y^2=x^3-268241043x-1899245436158$	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.?, $\ldots$	$[]$

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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 $\F_{q}$

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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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