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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
6930.e2	6930b1	6930.e	6930b	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$0.676529752$	$1$	$9$	$1536$	$0.082274$	$-1740992427/492800$	$0.84195$	$2.82370$	$[1, -1, 0, -75, 325]$	$y^2+xy=x^3-x^2-75x+325$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(5, 5)]$
6930.bh2	6930u1	6930.bh	6930u	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$4608$	$0.631579$	$-1740992427/492800$	$0.84195$	$3.56906$	$[1, -1, 1, -677, -8099]$	$y^2+xy+y=x^3-x^2-677x-8099$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
34650.d2	34650a1	34650.d	34650a	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{8} \cdot 7 \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$4.304704789$	$1$	$3$	$110592$	$1.436298$	$-1740992427/492800$	$0.84195$	$3.94335$	$[1, -1, 0, -16917, -1029259]$	$y^2+xy=x^3-x^2-16917x-1029259$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(218, 2259)]$
34650.dj2	34650cn1	34650.dj	34650cn	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{8} \cdot 7 \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$0.586891794$	$1$	$9$	$36864$	$0.886992$	$-1740992427/492800$	$0.84195$	$3.31275$	$[1, -1, 1, -1880, 38747]$	$y^2+xy+y=x^3-x^2-1880x+38747$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(9, 145)]$
48510.bx2	48510k1	48510.bx	48510k	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{2} \cdot 7^{7} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$73728$	$1.055229$	$-1740992427/492800$	$0.84195$	$3.39655$	$[1, -1, 0, -3684, -104112]$	$y^2+xy=x^3-x^2-3684x-104112$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
48510.cl2	48510cb1	48510.cl	48510cb	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{2} \cdot 7^{7} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$0.599369124$	$1$	$9$	$221184$	$1.604534$	$-1740992427/492800$	$0.84195$	$4.00749$	$[1, -1, 1, -33158, 2844181]$	$y^2+xy+y=x^3-x^2-33158x+2844181$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(65, 947)]$
55440.h2	55440bv1	55440.h	55440bv	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{20} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$36864$	$0.775421$	$-1740992427/492800$	$0.84195$	$3.04764$	$[0, 0, 0, -1203, -19598]$	$y^2=x^3-1203x-19598$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
55440.dn2	55440ci1	55440.dn	55440ci	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{20} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$110592$	$1.324726$	$-1740992427/492800$	$0.84195$	$3.65110$	$[0, 0, 0, -10827, 529146]$	$y^2=x^3-10827x+529146$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
76230.br2	76230h1	76230.br	76230h	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{8} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$3.633329002$	$1$	$5$	$552960$	$1.830528$	$-1740992427/492800$	$0.84195$	$4.08760$	$[1, -1, 0, -81879, 11025053]$	$y^2+xy=x^3-x^2-81879x+11025053$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(-203, 4489)]$
76230.dd2	76230cs1	76230.dd	76230cs	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{8} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1.256683297$	$1$	$7$	$184320$	$1.281221$	$-1740992427/492800$	$0.84195$	$3.50123$	$[1, -1, 1, -9098, -405303]$	$y^2+xy+y=x^3-x^2-9098x-405303$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(201, 2319)]$
221760.bf2	221760hm1	221760.bf	221760hm	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{26} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$884736$	$1.671301$	$-1740992427/492800$	$0.84195$	$3.57777$	$[0, 0, 0, -43308, 4233168]$	$y^2=x^3-43308x+4233168$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
221760.gd2	221760nn1	221760.gd	221760nn	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{26} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$13.31263113$	$1$	$1$	$884736$	$1.671301$	$-1740992427/492800$	$0.84195$	$3.57777$	$[0, 0, 0, -43308, -4233168]$	$y^2=x^3-43308x-4233168$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(19308262/19, 84842114048/19)]$
221760.ji2	221760gh1	221760.ji	221760gh	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{26} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$294912$	$1.121994$	$-1740992427/492800$	$0.84195$	$3.04227$	$[0, 0, 0, -4812, -156784]$	$y^2=x^3-4812x-156784$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
221760.lw2	221760mw1	221760.lw	221760mw	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{26} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$2.857595869$	$1$	$3$	$294912$	$1.121994$	$-1740992427/492800$	$0.84195$	$3.04227$	$[0, 0, 0, -4812, 156784]$	$y^2=x^3-4812x+156784$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(53, 225)]$
242550.bg2	242550bg1	242550.bg	242550bg	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{8} \cdot 7^{7} \cdot 11 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$6.535264093$	$1$	$11$	$5308416$	$2.409252$	$-1740992427/492800$	$0.84195$	$4.26612$	$[1, -1, 0, -828942, 354693716]$	$y^2+xy=x^3-x^2-828942x+354693716$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(149, 15238), (524, 7738)]$
242550.mn2	242550mn1	242550.mn	242550mn	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{8} \cdot 7^{7} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$1769472$	$1.859947$	$-1740992427/492800$	$0.84195$	$3.73449$	$[1, -1, 1, -92105, -13106103]$	$y^2+xy+y=x^3-x^2-92105x-13106103$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
277200.jx2	277200jx1	277200.jx	277200jx	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{20} \cdot 3^{3} \cdot 5^{8} \cdot 7 \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$6.314707531$	$1$	$1$	$884736$	$1.580139$	$-1740992427/492800$	$0.84195$	$3.42678$	$[0, 0, 0, -30075, -2449750]$	$y^2=x^3-30075x-2449750$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(4505/4, 216125/4)]$
277200.mv2	277200mv1	277200.mv	277200mv	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{20} \cdot 3^{9} \cdot 5^{8} \cdot 7 \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$2654208$	$2.129444$	$-1740992427/492800$	$0.84195$	$3.95275$	$[0, 0, 0, -270675, 66143250]$	$y^2=x^3-270675x+66143250$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
381150.fl2	381150fl1	381150.fl	381150fl	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{8} \cdot 3^{3} \cdot 5^{8} \cdot 7 \cdot 11^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$3.331269408$	$1$	$5$	$4423680$	$2.085941$	$-1740992427/492800$	$0.84195$	$3.81417$	$[1, -1, 0, -227442, -50890284]$	$y^2+xy=x^3-x^2-227442x-50890284$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(964, 24518)]$
381150.nz2	381150nz1	381150.nz	381150nz	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{8} \cdot 3^{9} \cdot 5^{8} \cdot 7 \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$13271040$	$2.635246$	$-1740992427/492800$	$0.84195$	$4.32711$	$[1, -1, 1, -2046980, 1376084647]$	$y^2+xy+y=x^3-x^2-2046980x+1376084647$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
388080.gb2	388080gb1	388080.gb	388080gb	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{20} \cdot 3^{9} \cdot 5^{2} \cdot 7^{7} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$5308416$	$2.297684$	$-1740992427/492800$	$0.84195$	$4.00628$	$[0, 0, 0, -530523, -181497078]$	$y^2=x^3-530523x-181497078$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$
388080.kf2	388080kf1	388080.kf	388080kf	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{20} \cdot 3^{3} \cdot 5^{2} \cdot 7^{7} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$1769472$	$1.748375$	$-1740992427/492800$	$0.84195$	$3.49406$	$[0, 0, 0, -58947, 6722114]$	$y^2=x^3-58947x+6722114$	2.3.0.a.1, 60.6.0.b.1, 462.6.0.?, 1540.6.0.?, 4620.12.0.?	$[]$

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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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