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 (23 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	Semistable	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
3570.c2	3570c1	3570.c	3570c	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{3} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$14280$	$12$	$0$	$0.277541288$	$1$	$13$	$1152$	$0.206118$	$59822347031/83966400$	$0.88512$	$3.07679$	$[1, 1, 0, 82, 372]$	$y^2+xy=x^3+x^2+82x+372$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(4, 26)]$
10710.bj2	10710bm1	10710.bj	10710bm	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{6} \cdot 3^{8} \cdot 5^{2} \cdot 7^{3} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$0.339799334$	$1$	$13$	$9216$	$0.755424$	$59822347031/83966400$	$0.88512$	$3.42289$	$[1, -1, 1, 733, -9309]$	$y^2+xy+y=x^3-x^2+733x-9309$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(29, 174)]$
17850.bt2	17850bp1	17850.bt	17850bp	$2$	$2$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ - 2^{6} \cdot 3^{2} \cdot 5^{8} \cdot 7^{3} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1.319320646$	$1$	$7$	$27648$	$1.010838$	$59822347031/83966400$	$0.88512$	$3.55736$	$[1, 0, 0, 2037, 42417]$	$y^2+xy=x^3+2037x+42417$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(32, 359)]$
24990.bi2	24990bf1	24990.bi	24990bf	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{9} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1$	$1$	$1$	$55296$	$1.179073$	$59822347031/83966400$	$0.88512$	$3.63853$	$[1, 0, 1, 3992, -115594]$	$y^2+xy+y=x^3+3992x-115594$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[]$
28560.cj2	28560dh1	28560.cj	28560dh	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 7^{3} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1$	$1$	$1$	$27648$	$0.899265$	$59822347031/83966400$	$0.88512$	$3.26390$	$[0, 1, 0, 1304, -21196]$	$y^2=x^3+x^2+1304x-21196$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[]$
53550.k2	53550be1	53550.k	53550be	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 $	$ - 2^{6} \cdot 3^{8} \cdot 5^{8} \cdot 7^{3} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1.830830398$	$1$	$5$	$221184$	$1.560143$	$59822347031/83966400$	$0.88512$	$3.80382$	$[1, -1, 0, 18333, -1145259]$	$y^2+xy=x^3-x^2+18333x-1145259$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(174, 2613)]$
60690.z2	60690z1	60690.z	60690z	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17^{2} $	$ - 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{3} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$4.193225161$	$1$	$5$	$331776$	$1.622725$	$59822347031/83966400$	$0.88512$	$3.82878$	$[1, 0, 1, 23547, 1662448]$	$y^2+xy+y=x^3+23547x+1662448$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(-53, 542)]$
74970.ch2	74970cy1	74970.ch	74970cy	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{8} \cdot 5^{2} \cdot 7^{9} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$0.711587604$	$1$	$9$	$442368$	$1.728380$	$59822347031/83966400$	$0.88512$	$3.86965$	$[1, -1, 1, 35932, 3121031]$	$y^2+xy+y=x^3-x^2+35932x+3121031$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(-5, 1717)]$
85680.eb2	85680ew1	85680.eb	85680ew	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{18} \cdot 3^{8} \cdot 5^{2} \cdot 7^{3} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1$	$1$	$1$	$221184$	$1.448572$	$59822347031/83966400$	$0.88512$	$3.52855$	$[0, 0, 0, 11733, 584026]$	$y^2=x^3+11733x+584026$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[]$
114240.dr2	114240ha1	114240.dr	114240ha	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{24} \cdot 3^{2} \cdot 5^{2} \cdot 7^{3} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1$	$1$	$1$	$221184$	$1.245838$	$59822347031/83966400$	$0.88512$	$3.23249$	$[0, -1, 0, 5215, -174783]$	$y^2=x^3-x^2+5215x-174783$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[]$
114240.ki2	114240ex1	114240.ki	114240ex	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{24} \cdot 3^{2} \cdot 5^{2} \cdot 7^{3} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1.850699250$	$1$	$5$	$221184$	$1.245838$	$59822347031/83966400$	$0.88512$	$3.23249$	$[0, 1, 0, 5215, 174783]$	$y^2=x^3+x^2+5215x+174783$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(-14, 315)]$
124950.fy2	124950fn1	124950.fy	124950fn	$2$	$2$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{2} \cdot 5^{8} \cdot 7^{9} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1$	$1$	$1$	$1327104$	$1.983793$	$59822347031/83966400$	$0.88512$	$3.96238$	$[1, 1, 1, 99812, -14449219]$	$y^2+xy+y=x^3+x^2+99812x-14449219$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[]$
142800.dh2	142800ds1	142800.dh	142800ds	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ - 2^{18} \cdot 3^{2} \cdot 5^{8} \cdot 7^{3} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1.147962114$	$1$	$7$	$663552$	$1.703985$	$59822347031/83966400$	$0.88512$	$3.63491$	$[0, -1, 0, 32592, -2714688]$	$y^2=x^3-x^2+32592x-2714688$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(122, 1750)]$
182070.ci2	182070bn1	182070.ci	182070bn	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17^{2} $	$ - 2^{6} \cdot 3^{8} \cdot 5^{2} \cdot 7^{3} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1.461847160$	$1$	$7$	$2654208$	$2.172031$	$59822347031/83966400$	$0.88512$	$4.02572$	$[1, -1, 1, 211927, -44886103]$	$y^2+xy+y=x^3-x^2+211927x-44886103$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(523, 14188)]$
199920.cv2	199920ch1	199920.cv	199920ch	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 $	$ - 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 7^{9} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1$	$1$	$1$	$1327104$	$1.872221$	$59822347031/83966400$	$0.88512$	$3.70011$	$[0, -1, 0, 63880, 7398000]$	$y^2=x^3-x^2+63880x+7398000$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[]$
303450.ey2	303450ey1	303450.ey	303450ey	$2$	$2$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17^{2} $	$ - 2^{6} \cdot 3^{2} \cdot 5^{8} \cdot 7^{3} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$0.563475519$	$1$	$9$	$7962624$	$2.427444$	$59822347031/83966400$	$0.88512$	$4.10561$	$[1, 1, 1, 588687, 207806031]$	$y^2+xy+y=x^3+x^2+588687x+207806031$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(-101, 12188)]$
342720.bn2	342720bn1	342720.bn	342720bn	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{24} \cdot 3^{8} \cdot 5^{2} \cdot 7^{3} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$3.240656664$	$1$	$5$	$1769472$	$1.795145$	$59822347031/83966400$	$0.88512$	$3.47105$	$[0, 0, 0, 46932, 4672208]$	$y^2=x^3+46932x+4672208$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(-68, 1080)]$
342720.gk2	342720gk1	342720.gk	342720gk	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{24} \cdot 3^{8} \cdot 5^{2} \cdot 7^{3} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1.761822487$	$1$	$7$	$1769472$	$1.795145$	$59822347031/83966400$	$0.88512$	$3.47105$	$[0, 0, 0, 46932, -4672208]$	$y^2=x^3+46932x-4672208$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(342, 7168)]$
374850.cm2	374850cm1	374850.cm	374850cm	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{8} \cdot 5^{8} \cdot 7^{9} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$2.574065088$	$1$	$5$	$10616832$	$2.533100$	$59822347031/83966400$	$0.88512$	$4.13680$	$[1, -1, 0, 898308, 391027216]$	$y^2+xy=x^3-x^2+898308x+391027216$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(359, 27383)]$
424830.l2	424830l1	424830.l	424830l	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{2} $	$ - 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{9} \cdot 17^{7} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$6.323171164$	$1$	$17$	$15925248$	$2.595680$	$59822347031/83966400$	$0.88512$	$4.15480$	$[1, 1, 0, 1153827, -569065923]$	$y^2+xy=x^3+x^2+1153827x-569065923$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(834, 30795), (3146, 183387)]$
428400.mo2	428400mo1	428400.mo	428400mo	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 $	$ - 2^{18} \cdot 3^{8} \cdot 5^{8} \cdot 7^{3} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1.333551572$	$1$	$7$	$5308416$	$2.253292$	$59822347031/83966400$	$0.88512$	$3.83528$	$[0, 0, 0, 293325, 73003250]$	$y^2=x^3+293325x+73003250$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(55, 9450)]$
431970.dz2	431970dz1	431970.dz	431970dz	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 17 $	$ - 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{3} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$2.853138428$	$1$	$5$	$1612800$	$1.405066$	$59822347031/83966400$	$0.88512$	$3.04841$	$[1, 1, 1, 9859, -445741]$	$y^2+xy+y=x^3+x^2+9859x-445741$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[(99, 1180)]$
485520.du2	485520du1	485520.du	485520du	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 17^{2} $	$ - 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 7^{3} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$14280$	$12$	$0$	$1$	$1$	$1$	$7962624$	$2.315872$	$59822347031/83966400$	$0.88512$	$3.85597$	$[0, -1, 0, 376760, -106396688]$	$y^2=x^3-x^2+376760x-106396688$	2.3.0.a.1, 120.6.0.?, 238.6.0.?, 14280.12.0.?	$[]$

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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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