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.b1	24960bc2	24960.b	24960bc	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13 $	$ 2^{13} \cdot 3^{20} \cdot 5^{5} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3120$	$48$	$0$	$6.164828628$	$1$		$3$	$358400$	$2.177967$	$601942297084171232/141650616290625$	$1.01463$	$4.93330$	$[0, -1, 0, -354601, 62724601]$	$y^2=x^3-x^2-354601x+62724601$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.1, 520.12.0.?, 1040.24.0.?, $\ldots$	$[(-585, 8344)]$
24960.x1	24960f1	24960.x	24960f	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13 $	$ 2^{7} \cdot 3^{20} \cdot 5^{5} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3120$	$48$	$0$	$1$	$4$	$2$	$1$	$179200$	$1.831394$	$601942297084171232/141650616290625$	$1.01463$	$4.52255$	$[0, -1, 0, -88650, -7796250]$	$y^2=x^3-x^2-88650x-7796250$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 520.12.0.?, 1040.24.0.?, $\ldots$	$[ ]$
24960.bl1	24960o2	24960.bl	24960o	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13 $	$ 2^{13} \cdot 3^{20} \cdot 5^{5} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3120$	$48$	$0$	$3.535287430$	$1$		$5$	$358400$	$2.177967$	$601942297084171232/141650616290625$	$1.01463$	$4.93330$	$[0, 1, 0, -354601, -62724601]$	$y^2=x^3+x^2-354601x-62724601$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.1, 520.12.0.?, 1040.24.0.?, $\ldots$	$[(-235, 2772)]$
24960.bp1	24960r1	24960.bp	24960r	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13 $	$ 2^{7} \cdot 3^{20} \cdot 5^{5} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3120$	$48$	$0$	$0.639395336$	$1$		$5$	$179200$	$1.831394$	$601942297084171232/141650616290625$	$1.01463$	$4.52255$	$[0, 1, 0, -88650, 7796250]$	$y^2=x^3+x^2-88650x+7796250$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 520.12.0.?, 1040.24.0.?, $\ldots$	$[(-225, 4050)]$
74880.b1	74880db1	74880.b	74880db	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 13 $	$ 2^{7} \cdot 3^{26} \cdot 5^{5} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.22	2B	$1040$	$48$	$0$	$23.54283088$	$1$		$1$	$1433600$	$2.380699$	$601942297084171232/141650616290625$	$1.01463$	$4.66717$	$[0, 0, 0, -797853, -211296602]$	$y^2=x^3-797853x-211296602$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 520.24.0.?, 1040.48.0.?	$[(11558538321/3266, 488362931837231/3266)]$
74880.br1	74880cx1	74880.br	74880cx	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 13 $	$ 2^{7} \cdot 3^{26} \cdot 5^{5} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.22	2B	$1040$	$48$	$0$	$35.80679371$	$1$		$1$	$1433600$	$2.380699$	$601942297084171232/141650616290625$	$1.01463$	$4.66717$	$[0, 0, 0, -797853, 211296602]$	$y^2=x^3-797853x+211296602$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 520.24.0.?, 1040.48.0.?	$[(3280977439506601/1164138, 176173932822168814004269/1164138)]$
74880.cf1	74880cc2	74880.cf	74880cc	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 13 $	$ 2^{13} \cdot 3^{26} \cdot 5^{5} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.21	2B	$1040$	$48$	$0$	$1$	$1$		$1$	$2867200$	$2.727272$	$601942297084171232/141650616290625$	$1.01463$	$5.03772$	$[0, 0, 0, -3191412, -1690372816]$	$y^2=x^3-3191412x-1690372816$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 520.24.0.?, 1040.48.0.?	$[ ]$
74880.dj1	74880dq2	74880.dj	74880dq	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5 \cdot 13 $	$ 2^{13} \cdot 3^{26} \cdot 5^{5} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.21	2B	$1040$	$48$	$0$	$5.935260684$	$1$		$3$	$2867200$	$2.727272$	$601942297084171232/141650616290625$	$1.01463$	$5.03772$	$[0, 0, 0, -3191412, 1690372816]$	$y^2=x^3-3191412x+1690372816$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 520.24.0.?, 1040.48.0.?	$[(2277, 78925)]$
124800.g1	124800di2	124800.g	124800di	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{13} \cdot 3^{20} \cdot 5^{11} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3120$	$48$	$0$	$1$	$4$	$2$	$1$	$8601600$	$2.982685$	$601942297084171232/141650616290625$	$1.01463$	$5.07961$	$[0, -1, 0, -8865033, -7822845063]$	$y^2=x^3-x^2-8865033x-7822845063$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 312.12.0.?, 520.12.0.?, $\ldots$	$[ ]$
124800.cq1	124800dt1	124800.cq	124800dt	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{7} \cdot 3^{20} \cdot 5^{11} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3120$	$48$	$0$	$23.65118328$	$1$		$1$	$4300800$	$2.636112$	$601942297084171232/141650616290625$	$1.01463$	$4.72519$	$[0, -1, 0, -2216258, 978963762]$	$y^2=x^3-x^2-2216258x+978963762$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 312.12.0.?, 520.12.0.?, $\ldots$	$[(2617143877/7829, 14270700834555550/7829)]$
124800.dc1	124800ey1	124800.dc	124800ey	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{7} \cdot 3^{20} \cdot 5^{11} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3120$	$48$	$0$	$1$	$1$		$1$	$4300800$	$2.636112$	$601942297084171232/141650616290625$	$1.01463$	$4.72519$	$[0, 1, 0, -2216258, -978963762]$	$y^2=x^3+x^2-2216258x-978963762$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 312.12.0.?, 520.12.0.?, $\ldots$	$[ ]$
124800.fm1	124800bw2	124800.fm	124800bw	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{13} \cdot 3^{20} \cdot 5^{11} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3120$	$48$	$0$	$1$	$1$		$1$	$8601600$	$2.982685$	$601942297084171232/141650616290625$	$1.01463$	$5.07961$	$[0, 1, 0, -8865033, 7822845063]$	$y^2=x^3+x^2-8865033x+7822845063$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 312.12.0.?, 520.12.0.?, $\ldots$	$[ ]$
324480.g1	324480g1	324480.g	324480g	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{7} \cdot 3^{20} \cdot 5^{5} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3120$	$48$	$0$	$1$	$16$	$2$	$1$	$30105600$	$3.113869$	$601942297084171232/141650616290625$	$1.01463$	$4.82118$	$[0, -1, 0, -14981906, -17188288794]$	$y^2=x^3-x^2-14981906x-17188288794$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 312.12.0.?, 520.12.0.?, $\ldots$	$[ ]$
324480.cz1	324480cz2	324480.cz	324480cz	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{13} \cdot 3^{20} \cdot 5^{5} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3120$	$48$	$0$	$1$	$1$		$1$	$60211200$	$3.460442$	$601942297084171232/141650616290625$	$1.01463$	$5.14891$	$[0, -1, 0, -59927625, 137566237977]$	$y^2=x^3-x^2-59927625x+137566237977$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 312.12.0.?, 520.12.0.?, $\ldots$	$[ ]$
324480.em1	324480em1	324480.em	324480em	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{7} \cdot 3^{20} \cdot 5^{5} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3120$	$48$	$0$	$12.23415309$	$1$		$1$	$30105600$	$3.113869$	$601942297084171232/141650616290625$	$1.01463$	$4.82118$	$[0, 1, 0, -14981906, 17188288794]$	$y^2=x^3+x^2-14981906x+17188288794$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 312.12.0.?, 520.12.0.?, $\ldots$	$[(179701/6, 55829305/6)]$
324480.ex1	324480ex2	324480.ex	324480ex	$2$	$2$	$ 2^{7} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{13} \cdot 3^{20} \cdot 5^{5} \cdot 13^{7} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3120$	$48$	$0$	$1.630680716$	$1$		$21$	$60211200$	$3.460442$	$601942297084171232/141650616290625$	$1.01463$	$5.14891$	$[0, 1, 0, -59927625, -137566237977]$	$y^2=x^3+x^2-59927625x-137566237977$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 312.12.0.?, 520.12.0.?, $\ldots$	$[(-2934, 114075), (19881, 2555280)]$
374400.ba1	374400ba2	374400.ba	374400ba	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{13} \cdot 3^{26} \cdot 5^{11} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1040$	$48$	$0$	$1$	$1$		$1$	$68812800$	$3.531994$	$601942297084171232/141650616290625$	$1.01463$	$5.15840$	$[0, 0, 0, -79785300, 211296602000]$	$y^2=x^3-79785300x+211296602000$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.3, 104.12.0.?, 520.24.0.?, $\ldots$	$[ ]$
374400.bg1	374400bg1	374400.bg	374400bg	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{7} \cdot 3^{26} \cdot 5^{11} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1040$	$48$	$0$	$29.18155939$	$1$		$1$	$34406400$	$3.185417$	$601942297084171232/141650616290625$	$1.01463$	$4.83432$	$[0, 0, 0, -19946325, 26412075250]$	$y^2=x^3-19946325x+26412075250$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.2, 104.12.0.?, 520.24.0.?, $\ldots$	$[(22507907558265/31186, 104891757582495624475/31186)]$
374400.kg1	374400kg2	374400.kg	374400kg	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{13} \cdot 3^{26} \cdot 5^{11} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1040$	$48$	$0$	$12.93589732$	$1$		$1$	$68812800$	$3.531994$	$601942297084171232/141650616290625$	$1.01463$	$5.15840$	$[0, 0, 0, -79785300, -211296602000]$	$y^2=x^3-79785300x-211296602000$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.3, 104.12.0.?, 520.24.0.?, $\ldots$	$[(119782490/49, 1288643647500/49)]$
374400.km1	374400km1	374400.km	374400km	$2$	$2$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{7} \cdot 3^{26} \cdot 5^{11} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1040$	$48$	$0$	$68.52679073$	$1$		$1$	$34406400$	$3.185417$	$601942297084171232/141650616290625$	$1.01463$	$4.83432$	$[0, 0, 0, -19946325, -26412075250]$	$y^2=x^3-19946325x-26412075250$	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.2, 104.12.0.?, 520.24.0.?, $\ldots$	$[(2126210009143544610808451762065/17578026790878, 2187220604023547044405541731993541890386760975/17578026790878)]$

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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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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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