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
10200.b2	10200n2	10200.b	10200n	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 17 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{3} \cdot 17^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$0.867210603$	$1$		$5$	$29952$	$1.262371$	$-1439609866256/651714363$	$0.96496$	$4.21952$	$[0, -1, 0, -7468, 334132]$	$y^2=x^3-x^2-7468x+334132$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[(-18, 680)]$
10200.bq2	10200bn2	10200.bq	10200bn	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 17 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{9} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$149760$	$2.067089$	$-1439609866256/651714363$	$0.96496$	$5.26573$	$[0, 1, 0, -186708, 41393088]$	$y^2=x^3+x^2-186708x+41393088$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$
20400.c2	20400o2	20400.c	20400o	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 17 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{9} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$299520$	$2.067089$	$-1439609866256/651714363$	$0.96496$	$4.89791$	$[0, -1, 0, -186708, -41393088]$	$y^2=x^3-x^2-186708x-41393088$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$
20400.dv2	20400bq2	20400.dv	20400bq	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 17 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{3} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$59904$	$1.262371$	$-1439609866256/651714363$	$0.96496$	$3.92478$	$[0, 1, 0, -7468, -334132]$	$y^2=x^3+x^2-7468x-334132$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$
30600.c2	30600cq2	30600.c	30600cq	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{3} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$239616$	$1.811678$	$-1439609866256/651714363$	$0.96496$	$4.40890$	$[0, 0, 0, -67215, -8954350]$	$y^2=x^3-67215x-8954350$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$
30600.cs2	30600bi2	30600.cs	30600bi	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{9} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$1198080$	$2.616398$	$-1439609866256/651714363$	$0.96496$	$5.34383$	$[0, 0, 0, -1680375, -1119293750]$	$y^2=x^3-1680375x-1119293750$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$
61200.o2	61200cw2	61200.o	61200cw	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{9} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$2396160$	$2.616398$	$-1439609866256/651714363$	$0.96496$	$5.00776$	$[0, 0, 0, -1680375, 1119293750]$	$y^2=x^3-1680375x+1119293750$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$
61200.hc2	61200ci2	61200.hc	61200ci	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{3} \cdot 17^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$2.775384549$	$1$		$3$	$479232$	$1.811678$	$-1439609866256/651714363$	$0.96496$	$4.13163$	$[0, 0, 0, -67215, 8954350]$	$y^2=x^3-67215x+8954350$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[(425, 7560)]$
81600.eq2	81600br2	81600.eq	81600br	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 17 $	$ - 2^{14} \cdot 3^{3} \cdot 5^{9} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$4$	$2$	$1$	$2396160$	$2.413666$	$-1439609866256/651714363$	$0.96496$	$4.66527$	$[0, -1, 0, -746833, 331891537]$	$y^2=x^3-x^2-746833x+331891537$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$
81600.et2	81600hp2	81600.et	81600hp	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 17 $	$ - 2^{14} \cdot 3^{3} \cdot 5^{3} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$479232$	$1.608946$	$-1439609866256/651714363$	$0.96496$	$3.81143$	$[0, -1, 0, -29873, -2643183]$	$y^2=x^3-x^2-29873x-2643183$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$
81600.fh2	81600fb2	81600.fh	81600fb	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 17 $	$ - 2^{14} \cdot 3^{3} \cdot 5^{3} \cdot 17^{6} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$0.706832263$	$1$		$25$	$479232$	$1.608946$	$-1439609866256/651714363$	$0.96496$	$3.81143$	$[0, 1, 0, -29873, 2643183]$	$y^2=x^3+x^2-29873x+2643183$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[(82, 867), (-173, 1632)]$
81600.fm2	81600jl2	81600.fm	81600jl	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 17 $	$ - 2^{14} \cdot 3^{3} \cdot 5^{9} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$2396160$	$2.413666$	$-1439609866256/651714363$	$0.96496$	$4.66527$	$[0, 1, 0, -746833, -331891537]$	$y^2=x^3+x^2-746833x-331891537$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$
173400.d2	173400bf2	173400.d	173400bf	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 17^{2} $	$ - 2^{8} \cdot 3^{3} \cdot 5^{9} \cdot 17^{12} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$3.467682687$	$1$		$3$	$43130880$	$3.483696$	$-1439609866256/651714363$	$0.96496$	$5.43818$	$[0, -1, 0, -53958708, 203687993412]$	$y^2=x^3-x^2-53958708x+203687993412$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[(10342, 867000)]$
173400.er2	173400cx2	173400.er	173400cx	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 17^{2} $	$ - 2^{8} \cdot 3^{3} \cdot 5^{3} \cdot 17^{12} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$6.453060608$	$1$		$3$	$8626176$	$2.678978$	$-1439609866256/651714363$	$0.96496$	$4.63769$	$[0, 1, 0, -2158348, 1628640608]$	$y^2=x^3+x^2-2158348x+1628640608$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[(-1708, 18312)]$
244800.bf2	244800bf2	244800.bf	244800bf	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{14} \cdot 3^{9} \cdot 5^{9} \cdot 17^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1.161424703$	$1$		$5$	$19169280$	$2.962971$	$-1439609866256/651714363$	$0.96496$	$4.78345$	$[0, 0, 0, -6721500, 8954350000]$	$y^2=x^3-6721500x+8954350000$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[(9650, 918000)]$
244800.bm2	244800bm2	244800.bm	244800bm	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{14} \cdot 3^{9} \cdot 5^{3} \cdot 17^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$4.176592644$	$1$		$3$	$3833856$	$2.158253$	$-1439609866256/651714363$	$0.96496$	$4.00520$	$[0, 0, 0, -268860, -71634800]$	$y^2=x^3-268860x-71634800$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[(1430, 49680)]$
244800.rs2	244800rs2	244800.rs	244800rs	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{14} \cdot 3^{9} \cdot 5^{3} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$1$		$1$	$3833856$	$2.158253$	$-1439609866256/651714363$	$0.96496$	$4.00520$	$[0, 0, 0, -268860, 71634800]$	$y^2=x^3-268860x+71634800$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$
244800.sk2	244800sk2	244800.sk	244800sk	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{14} \cdot 3^{9} \cdot 5^{9} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$4$	$2$	$1$	$19169280$	$2.962971$	$-1439609866256/651714363$	$0.96496$	$4.78345$	$[0, 0, 0, -6721500, -8954350000]$	$y^2=x^3-6721500x-8954350000$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$
346800.m2	346800m2	346800.m	346800m	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 17^{2} $	$ - 2^{8} \cdot 3^{3} \cdot 5^{3} \cdot 17^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$9$	$3$	$1$	$17252352$	$2.678978$	$-1439609866256/651714363$	$0.96496$	$4.38569$	$[0, -1, 0, -2158348, -1628640608]$	$y^2=x^3-x^2-2158348x-1628640608$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$
346800.lp2	346800lp2	346800.lp	346800lp	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 17^{2} $	$ - 2^{8} \cdot 3^{3} \cdot 5^{9} \cdot 17^{12} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$41.19238005$	$1$		$1$	$86261760$	$3.483696$	$-1439609866256/651714363$	$0.96496$	$5.14269$	$[0, 1, 0, -53958708, -203687993412]$	$y^2=x^3+x^2-53958708x-203687993412$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[(234600755184243166227/126281063, 2977838543493066885458582736750/126281063)]$
499800.dl2	499800dl2	499800.dl	499800dl	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{9} \cdot 7^{6} \cdot 17^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$9.115088272$	$1$		$1$	$43130880$	$3.040047$	$-1439609866256/651714363$	$0.96496$	$4.59374$	$[0, -1, 0, -9148708, -14216126588]$	$y^2=x^3-x^2-9148708x-14216126588$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[(1061053/3, 1092594250/3)]$
499800.hz2	499800hz2	499800.hz	499800hz	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{3} \cdot 7^{6} \cdot 17^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1020$	$12$	$0$	$1$	$4$	$2$	$1$	$8626176$	$2.235325$	$-1439609866256/651714363$	$0.96496$	$3.85782$	$[0, 1, 0, -365948, -113875392]$	$y^2=x^3+x^2-365948x-113875392$	2.3.0.a.1, 30.6.0.a.1, 204.6.0.?, 340.6.0.?, 1020.12.0.?	$[]$

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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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