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
24960.b2	24960bc1	24960.b	24960bc	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{8} \cdot 3^{10} \cdot 5^{10} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3120$	$48$	$0$	$3.082414314$	$1$		$3$	$179200$	$1.831394$	$59519748892520576/97453916015625$	$1.02150$	$4.42213$	$[0, -1, 0, 51649, 6093351]$	$y^2=x^3-x^2+51649x+6093351$	2.3.0.a.1, 4.6.0.a.1, 12.12.0-4.a.1.1, 520.12.0.?, 1040.24.0.?, $\ldots$	$[(293, 6804)]$
24960.x2	24960f2	24960.x	24960f	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{14} \cdot 3^{10} \cdot 5^{10} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3120$	$48$	$0$	$1$	$1$		$1$	$358400$	$2.177967$	$59519748892520576/97453916015625$	$1.02150$	$4.83288$	$[0, -1, 0, 206595, -48953403]$	$y^2=x^3-x^2+206595x-48953403$	2.3.0.a.1, 4.6.0.a.1, 24.12.0-4.a.1.1, 520.12.0.?, 780.12.0.?, $\ldots$	$[ ]$
24960.bl2	24960o1	24960.bl	24960o	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{8} \cdot 3^{10} \cdot 5^{10} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3120$	$48$	$0$	$1.767643715$	$1$		$5$	$179200$	$1.831394$	$59519748892520576/97453916015625$	$1.02150$	$4.42213$	$[0, 1, 0, 51649, -6093351]$	$y^2=x^3+x^2+51649x-6093351$	2.3.0.a.1, 4.6.0.a.1, 12.12.0-4.a.1.1, 520.12.0.?, 1040.24.0.?, $\ldots$	$[(112, 1053)]$
24960.bp2	24960r2	24960.bp	24960r	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{14} \cdot 3^{10} \cdot 5^{10} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3120$	$48$	$0$	$0.319697668$	$1$		$11$	$358400$	$2.177967$	$59519748892520576/97453916015625$	$1.02150$	$4.83288$	$[0, 1, 0, 206595, 48953403]$	$y^2=x^3+x^2+206595x+48953403$	2.3.0.a.1, 4.6.0.a.1, 24.12.0-4.a.1.1, 520.12.0.?, 780.12.0.?, $\ldots$	$[(126, 8775)]$
74880.b2	74880db2	74880.b	74880db	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{14} \cdot 3^{16} \cdot 5^{10} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.37	2B	$1040$	$48$	$0$	$11.77141544$	$1$		$1$	$2867200$	$2.727272$	$59519748892520576/97453916015625$	$1.02150$	$4.94713$	$[0, 0, 0, 1859352, -1319882528]$	$y^2=x^3+1859352x-1319882528$	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 260.12.0.?, 520.24.0.?, $\ldots$	$[(905081/23, 1008444879/23)]$
74880.br2	74880cx2	74880.br	74880cx	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{14} \cdot 3^{16} \cdot 5^{10} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.37	2B	$1040$	$48$	$0$	$17.90339685$	$1$		$1$	$2867200$	$2.727272$	$59519748892520576/97453916015625$	$1.02150$	$4.94713$	$[0, 0, 0, 1859352, 1319882528]$	$y^2=x^3+1859352x+1319882528$	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 260.12.0.?, 520.24.0.?, $\ldots$	$[(591649441/251, 14553444744891/251)]$
74880.cf2	74880cc1	74880.cf	74880cc	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{8} \cdot 3^{16} \cdot 5^{10} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.12	2B	$1040$	$48$	$0$	$1$	$1$		$1$	$1433600$	$2.380699$	$59519748892520576/97453916015625$	$1.02150$	$4.57658$	$[0, 0, 0, 464838, -164985316]$	$y^2=x^3+464838x-164985316$	2.3.0.a.1, 4.12.0-4.a.1.1, 520.24.0.?, 1040.48.0.?	$[ ]$
74880.dj2	74880dq1	74880.dj	74880dq	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{8} \cdot 3^{16} \cdot 5^{10} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.12	2B	$1040$	$48$	$0$	$2.967630342$	$1$		$5$	$1433600$	$2.380699$	$59519748892520576/97453916015625$	$1.02150$	$4.57658$	$[0, 0, 0, 464838, 164985316]$	$y^2=x^3+464838x+164985316$	2.3.0.a.1, 4.12.0-4.a.1.1, 520.24.0.?, 1040.48.0.?	$[(27, 13325)]$
124800.g2	124800di1	124800.g	124800di	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{10} \cdot 5^{16} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3120$	$48$	$0$	$1$	$1$		$1$	$4300800$	$2.636112$	$59519748892520576/97453916015625$	$1.02150$	$4.63854$	$[0, -1, 0, 1291217, -764251313]$	$y^2=x^3-x^2+1291217x-764251313$	2.3.0.a.1, 4.6.0.a.1, 60.12.0-4.a.1.1, 312.12.0.?, 520.12.0.?, $\ldots$	$[ ]$
124800.cq2	124800dt2	124800.cq	124800dt	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{14} \cdot 3^{10} \cdot 5^{16} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3120$	$48$	$0$	$11.82559164$	$1$		$1$	$8601600$	$2.982685$	$59519748892520576/97453916015625$	$1.02150$	$4.99296$	$[0, -1, 0, 5164867, 6108845637]$	$y^2=x^3-x^2+5164867x+6108845637$	2.3.0.a.1, 4.6.0.a.1, 120.12.0.?, 156.12.0.?, 520.12.0.?, $\ldots$	$[(19794287/37, 89232374088/37)]$
124800.dc2	124800ey2	124800.dc	124800ey	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{14} \cdot 3^{10} \cdot 5^{16} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3120$	$48$	$0$	$1$	$1$		$1$	$8601600$	$2.982685$	$59519748892520576/97453916015625$	$1.02150$	$4.99296$	$[0, 1, 0, 5164867, -6108845637]$	$y^2=x^3+x^2+5164867x-6108845637$	2.3.0.a.1, 4.6.0.a.1, 120.12.0.?, 156.12.0.?, 520.12.0.?, $\ldots$	$[ ]$
124800.fm2	124800bw1	124800.fm	124800bw	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{10} \cdot 5^{16} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3120$	$48$	$0$	$1$	$1$		$1$	$4300800$	$2.636112$	$59519748892520576/97453916015625$	$1.02150$	$4.63854$	$[0, 1, 0, 1291217, 764251313]$	$y^2=x^3+x^2+1291217x+764251313$	2.3.0.a.1, 4.6.0.a.1, 60.12.0-4.a.1.1, 312.12.0.?, 520.12.0.?, $\ldots$	$[ ]$
324480.g2	324480g2	324480.g	324480g	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{14} \cdot 3^{10} \cdot 5^{10} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3120$	$48$	$0$	$1$	$4$	$2$	$1$	$60211200$	$3.460442$	$59519748892520576/97453916015625$	$1.02150$	$5.06879$	$[0, -1, 0, 34914499, -107410968315]$	$y^2=x^3-x^2+34914499x-107410968315$	2.3.0.a.1, 4.6.0.a.1, 60.12.0-4.a.1.2, 312.12.0.?, 520.12.0.?, $\ldots$	$[ ]$
324480.cz2	324480cz1	324480.cz	324480cz	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{8} \cdot 3^{10} \cdot 5^{10} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3120$	$48$	$0$	$1$	$1$		$1$	$30105600$	$3.113869$	$59519748892520576/97453916015625$	$1.02150$	$4.74106$	$[0, -1, 0, 8728625, 13422006727]$	$y^2=x^3-x^2+8728625x+13422006727$	2.3.0.a.1, 4.6.0.a.1, 120.12.0.?, 156.12.0.?, 520.12.0.?, $\ldots$	$[ ]$
324480.em2	324480em2	324480.em	324480em	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{14} \cdot 3^{10} \cdot 5^{10} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3120$	$48$	$0$	$6.117076546$	$1$		$3$	$60211200$	$3.460442$	$59519748892520576/97453916015625$	$1.02150$	$5.06879$	$[0, 1, 0, 34914499, 107410968315]$	$y^2=x^3+x^2+34914499x+107410968315$	2.3.0.a.1, 4.6.0.a.1, 60.12.0-4.a.1.2, 312.12.0.?, 520.12.0.?, $\ldots$	$[(17190, 2405715)]$
324480.ex2	324480ex1	324480.ex	324480ex	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{8} \cdot 3^{10} \cdot 5^{10} \cdot 13^{8} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3120$	$48$	$0$	$1.630680716$	$1$		$21$	$30105600$	$3.113869$	$59519748892520576/97453916015625$	$1.02150$	$4.74106$	$[0, 1, 0, 8728625, -13422006727]$	$y^2=x^3+x^2+8728625x-13422006727$	2.3.0.a.1, 4.6.0.a.1, 120.12.0.?, 156.12.0.?, 520.12.0.?, $\ldots$	$[(2981, 197730), (1811, 91260)]$
374400.ba2	374400ba1	374400.ba	374400ba	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{16} \cdot 5^{16} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$1040$	$48$	$0$	$1$	$1$		$1$	$34406400$	$3.185417$	$59519748892520576/97453916015625$	$1.02150$	$4.75509$	$[0, 0, 0, 11620950, 20623164500]$	$y^2=x^3+11620950x+20623164500$	2.3.0.a.1, 4.6.0.a.1, 20.12.0-4.a.1.1, 104.12.0.?, 520.24.0.?, $\ldots$	$[ ]$
374400.bg2	374400bg2	374400.bg	374400bg	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{14} \cdot 3^{16} \cdot 5^{16} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$1040$	$48$	$0$	$14.59077969$	$1$		$1$	$68812800$	$3.531994$	$59519748892520576/97453916015625$	$1.02150$	$5.07917$	$[0, 0, 0, 46483800, 164985316000]$	$y^2=x^3+46483800x+164985316000$	2.3.0.a.1, 4.6.0.a.1, 40.12.0-4.a.1.1, 52.12.0-4.a.1.2, 520.24.0.?, $\ldots$	$[(88219460/31, 830973403800/31)]$
374400.kg2	374400kg1	374400.kg	374400kg	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{16} \cdot 5^{16} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$1040$	$48$	$0$	$25.87179464$	$1$		$1$	$34406400$	$3.185417$	$59519748892520576/97453916015625$	$1.02150$	$4.75509$	$[0, 0, 0, 11620950, -20623164500]$	$y^2=x^3+11620950x-20623164500$	2.3.0.a.1, 4.6.0.a.1, 20.12.0-4.a.1.1, 104.12.0.?, 520.24.0.?, $\ldots$	$[(2475796397380/27843, 4781022415976456650/27843)]$
374400.km2	374400km2	374400.km	374400km	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{14} \cdot 3^{16} \cdot 5^{16} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$1040$	$48$	$0$	$34.26339536$	$1$		$1$	$68812800$	$3.531994$	$59519748892520576/97453916015625$	$1.02150$	$5.07917$	$[0, 0, 0, 46483800, -164985316000]$	$y^2=x^3+46483800x-164985316000$	2.3.0.a.1, 4.6.0.a.1, 40.12.0-4.a.1.1, 52.12.0-4.a.1.2, 520.24.0.?, $\ldots$	$[(27632133685966060/1071773, 4747932198658338765283800/1071773)]$

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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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