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 (24 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
18720.a2	18720b1	18720.a	18720b	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.101340242$	$1$	$5$	$6144$	$0.331766$	$1728/325$	$0.96944$	$2.77329$	$[0, 0, 0, 27, -972]$	$y^2=x^3+27x-972$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(19, 80)]$
18720.v2	18720x1	18720.v	18720x	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$6144$	$0.331766$	$1728/325$	$0.96944$	$2.77329$	$[0, 0, 0, 27, 972]$	$y^2=x^3+27x+972$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
18720.y2	18720z1	18720.y	18720z	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.107593528$	$1$	$7$	$2048$	$-0.217540$	$1728/325$	$0.96944$	$2.10323$	$[0, 0, 0, 3, 36]$	$y^2=x^3+3x+36$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(0, 6)]$
18720.bs2	18720d1	18720.bs	18720d	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$2048$	$-0.217540$	$1728/325$	$0.96944$	$2.10323$	$[0, 0, 0, 3, -36]$	$y^2=x^3+3x-36$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
37440.d2	37440n1	37440.d	37440n	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 13 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.186325245$	$1$	$21$	$8192$	$0.129034$	$1728/325$	$0.96944$	$2.35972$	$[0, 0, 0, 12, 288]$	$y^2=x^3+12x+288$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(4, 20), (-2, 16)]$
37440.cv2	37440m1	37440.cv	37440m	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$8192$	$0.129034$	$1728/325$	$0.96944$	$2.35972$	$[0, 0, 0, 12, -288]$	$y^2=x^3+12x-288$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
37440.df2	37440bb1	37440.df	37440bb	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{12} \cdot 3^{9} \cdot 5^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.421017966$	$1$	$5$	$24576$	$0.678340$	$1728/325$	$0.96944$	$2.98568$	$[0, 0, 0, 108, -7776]$	$y^2=x^3+108x-7776$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(45, 297)]$
37440.fq2	37440ba1	37440.fq	37440ba	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{12} \cdot 3^{9} \cdot 5^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.954118257$	$1$	$5$	$24576$	$0.678340$	$1728/325$	$0.96944$	$2.98568$	$[0, 0, 0, 108, 7776]$	$y^2=x^3+108x+7776$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(-8, 80)]$
93600.g2	93600cx1	93600.g	93600cx	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.521174952$	$1$	$7$	$49152$	$0.587179$	$1728/325$	$0.96944$	$2.65112$	$[0, 0, 0, 75, -4500]$	$y^2=x^3+75x-4500$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(40, 250)]$
93600.n2	93600h1	93600.n	93600h	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{8} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$147456$	$1.136484$	$1728/325$	$0.96944$	$3.22697$	$[0, 0, 0, 675, 121500]$	$y^2=x^3+675x+121500$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
93600.eq2	93600cw1	93600.eq	93600cw	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$5.597325419$	$1$	$1$	$147456$	$1.136484$	$1728/325$	$0.96944$	$3.22697$	$[0, 0, 0, 675, -121500]$	$y^2=x^3+675x-121500$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(1615/3, 64900/3)]$
93600.ex2	93600g1	93600.ex	93600g	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{8} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$49152$	$0.587179$	$1728/325$	$0.96944$	$2.65112$	$[0, 0, 0, 75, 4500]$	$y^2=x^3+75x+4500$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
187200.n2	187200oz1	187200.n	187200oz	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{12} \cdot 3^{9} \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.610284114$	$1$	$5$	$589824$	$1.483059$	$1728/325$	$0.96944$	$3.38530$	$[0, 0, 0, 2700, 972000]$	$y^2=x^3+2700x+972000$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(10, 1000)]$
187200.bo2	187200pa1	187200.bo	187200pa	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{12} \cdot 3^{3} \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.856297820$	$1$	$5$	$196608$	$0.933752$	$1728/325$	$0.96944$	$2.84233$	$[0, 0, 0, 300, -36000]$	$y^2=x^3+300x-36000$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(40, 200)]$
187200.ou2	187200qk1	187200.ou	187200qk	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{12} \cdot 3^{3} \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.339286297$	$1$	$5$	$196608$	$0.933752$	$1728/325$	$0.96944$	$2.84233$	$[0, 0, 0, 300, 36000]$	$y^2=x^3+300x+36000$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(45, 375)]$
187200.px2	187200qn1	187200.px	187200qn	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{12} \cdot 3^{9} \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$4.824089642$	$1$	$3$	$589824$	$1.483059$	$1728/325$	$0.96944$	$3.38530$	$[0, 0, 0, 2700, -972000]$	$y^2=x^3+2700x-972000$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(286, 4816)]$
243360.j2	243360j1	243360.j	243360j	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$344064$	$1.064934$	$1728/325$	$0.96944$	$2.90913$	$[0, 0, 0, 507, -79092]$	$y^2=x^3+507x-79092$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
243360.co2	243360co1	243360.co	243360co	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$3.092547029$	$1$	$5$	$344064$	$1.064934$	$1728/325$	$0.96944$	$2.90913$	$[0, 0, 0, 507, 79092]$	$y^2=x^3+507x+79092$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(-29, 200)]$
243360.cv2	243360cv1	243360.cv	243360cv	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{6} \cdot 3^{9} \cdot 5^{2} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$1032192$	$1.614241$	$1728/325$	$0.96944$	$3.44062$	$[0, 0, 0, 4563, 2135484]$	$y^2=x^3+4563x+2135484$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
243360.fh2	243360fh1	243360.fh	243360fh	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{6} \cdot 3^{9} \cdot 5^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$13.19767432$	$1$	$1$	$1032192$	$1.614241$	$1728/325$	$0.96944$	$3.44062$	$[0, 0, 0, 4563, -2135484]$	$y^2=x^3+4563x-2135484$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(1095247/81, 962199620/81)]$
486720.v2	486720v1	486720.v	486720v	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{12} \cdot 3^{9} \cdot 5^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.215736255$	$1$	$7$	$4128768$	$1.960814$	$1728/325$	$0.96944$	$3.57609$	$[0, 0, 0, 18252, 17083872]$	$y^2=x^3+18252x+17083872$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(117, 4563)]$
486720.hp2	486720hp1	486720.hp	486720hp	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{12} \cdot 3^{9} \cdot 5^{2} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$3.580184056$	$1$	$5$	$4128768$	$1.960814$	$1728/325$	$0.96944$	$3.57609$	$[0, 0, 0, 18252, -17083872]$	$y^2=x^3+18252x-17083872$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(342, 5400)]$
486720.iy2	486720iy1	486720.iy	486720iy	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 13^{7} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$3.379027236$	$1$	$13$	$1376256$	$1.411509$	$1728/325$	$0.96944$	$3.07273$	$[0, 0, 0, 2028, -632736]$	$y^2=x^3+2028x-632736$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(130, 1352), (90, 528)]$
486720.qo2	486720qo1	486720.qo	486720qo	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$	$1$	$1376256$	$1.411509$	$1728/325$	$0.96944$	$3.07273$	$[0, 0, 0, 2028, 632736]$	$y^2=x^3+2028x+632736$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$

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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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