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 (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
81120.a1	81120g2	81120.a	81120g	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{12} \cdot 3^{3} \cdot 5^{4} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$1677312$	$2.160862$	$150568768/16875$	$0.91075$	$4.44388$	$[0, -1, 0, -389601, 84179601]$	$y^2=x^3-x^2-389601x+84179601$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[]$
81120.ba1	81120bn2	81120.ba	81120bn	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{12} \cdot 3^{3} \cdot 5^{4} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$129024$	$0.878386$	$150568768/16875$	$0.91075$	$3.08241$	$[0, -1, 0, -2305, 39025]$	$y^2=x^3-x^2-2305x+39025$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[]$
81120.bp1	81120bt2	81120.bp	81120bt	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{12} \cdot 3^{3} \cdot 5^{4} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$4$	$2$	$1$	$1677312$	$2.160862$	$150568768/16875$	$0.91075$	$4.44388$	$[0, 1, 0, -389601, -84179601]$	$y^2=x^3+x^2-389601x-84179601$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[]$
81120.br1	81120y2	81120.br	81120y	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{12} \cdot 3^{3} \cdot 5^{4} \cdot 13^{3} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.729605226$	$1$		$25$	$129024$	$0.878386$	$150568768/16875$	$0.91075$	$3.08241$	$[0, 1, 0, -2305, -39025]$	$y^2=x^3+x^2-2305x-39025$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[(-25, 60), (55, 60)]$
162240.f2	162240hr1	162240.f	162240hr	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{6} \cdot 3^{3} \cdot 5^{4} \cdot 13^{3} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$9.580420543$	$1$		$5$	$129024$	$0.531813$	$150568768/16875$	$0.91075$	$2.55765$	$[0, -1, 0, -576, -4590]$	$y^2=x^3-x^2-576x-4590$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[(35, 130), (157/2, 1425/2)]$
162240.eb2	162240hl1	162240.eb	162240hl	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{6} \cdot 3^{3} \cdot 5^{4} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$12.36684122$	$1$		$1$	$1677312$	$1.814287$	$150568768/16875$	$0.91075$	$3.84046$	$[0, -1, 0, -97400, -10473750]$	$y^2=x^3-x^2-97400x-10473750$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[(-205751/32, 31843525/32)]$
162240.ga2	162240gp1	162240.ga	162240gp	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{6} \cdot 3^{3} \cdot 5^{4} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$2.272849032$	$1$		$3$	$129024$	$0.531813$	$150568768/16875$	$0.91075$	$2.55765$	$[0, 1, 0, -576, 4590]$	$y^2=x^3+x^2-576x+4590$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[(69, 546)]$
162240.gj2	162240em1	162240.gj	162240em	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{6} \cdot 3^{3} \cdot 5^{4} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$1677312$	$1.814287$	$150568768/16875$	$0.91075$	$3.84046$	$[0, 1, 0, -97400, 10473750]$	$y^2=x^3+x^2-97400x+10473750$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[]$
243360.e1	243360e2	243360.e	243360e	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{12} \cdot 3^{9} \cdot 5^{4} \cdot 13^{3} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$2.595309921$	$1$		$15$	$1032192$	$1.427692$	$150568768/16875$	$0.91075$	$3.34085$	$[0, 0, 0, -20748, 1032928]$	$y^2=x^3-20748x+1032928$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[(29, 675), (56, 216)]$
243360.cp1	243360cp2	243360.cp	243360cp	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{12} \cdot 3^{9} \cdot 5^{4} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$2.819607529$	$1$		$5$	$1032192$	$1.427692$	$150568768/16875$	$0.91075$	$3.34085$	$[0, 0, 0, -20748, -1032928]$	$y^2=x^3-20748x-1032928$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[(-68, 252)]$
243360.cz1	243360cz2	243360.cz	243360cz	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{12} \cdot 3^{9} \cdot 5^{4} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$5.918576179$	$1$		$3$	$13418496$	$2.710167$	$150568768/16875$	$0.91075$	$4.58172$	$[0, 0, 0, -3506412, -2269342816]$	$y^2=x^3-3506412x-2269342816$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[(33800, 6204328)]$
243360.fe1	243360fe2	243360.fe	243360fe	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{12} \cdot 3^{9} \cdot 5^{4} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$13418496$	$2.710167$	$150568768/16875$	$0.91075$	$4.58172$	$[0, 0, 0, -3506412, 2269342816]$	$y^2=x^3-3506412x+2269342816$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[]$
405600.p1	405600p2	405600.p	405600p	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{12} \cdot 3^{3} \cdot 5^{10} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$4$	$2$	$1$	$40255488$	$2.965580$	$150568768/16875$	$0.91075$	$4.63783$	$[0, -1, 0, -9740033, -10502970063]$	$y^2=x^3-x^2-9740033x-10502970063$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[]$
405600.dh1	405600dh2	405600.dh	405600dh	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{12} \cdot 3^{3} \cdot 5^{10} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$6.492705974$	$1$		$1$	$3096576$	$1.683105$	$150568768/16875$	$0.91075$	$3.44604$	$[0, -1, 0, -57633, -4762863]$	$y^2=x^3-x^2-57633x-4762863$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[(-403/2, 833/2)]$
405600.dy1	405600dy2	405600.dy	405600dy	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{12} \cdot 3^{3} \cdot 5^{10} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.948858559$	$1$		$9$	$3096576$	$1.683105$	$150568768/16875$	$0.91075$	$3.44604$	$[0, 1, 0, -57633, 4762863]$	$y^2=x^3+x^2-57633x+4762863$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[(303, 3900)]$
405600.gr1	405600gr2	405600.gr	405600gr	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{12} \cdot 3^{3} \cdot 5^{10} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$40255488$	$2.965580$	$150568768/16875$	$0.91075$	$4.63783$	$[0, 1, 0, -9740033, 10502970063]$	$y^2=x^3+x^2-9740033x+10502970063$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[]$
486720.o2	486720o1	486720.o	486720o	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{6} \cdot 3^{9} \cdot 5^{4} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$7.190480979$	$1$		$1$	$13418496$	$2.363594$	$150568768/16875$	$0.91075$	$4.02163$	$[0, 0, 0, -876603, -283667852]$	$y^2=x^3-876603x-283667852$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[(4521/2, 104125/2)]$
486720.hx2	486720hx1	486720.hx	486720hx	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{6} \cdot 3^{9} \cdot 5^{4} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$24.65194415$	$1$		$1$	$13418496$	$2.363594$	$150568768/16875$	$0.91075$	$4.02163$	$[0, 0, 0, -876603, 283667852]$	$y^2=x^3-876603x+283667852$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[(244228432681/18966, 8303611283135875/18966)]$
486720.jb2	486720jb1	486720.jb	486720jb	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{6} \cdot 3^{9} \cdot 5^{4} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$1032192$	$1.081118$	$150568768/16875$	$0.91075$	$2.84644$	$[0, 0, 0, -5187, 129116]$	$y^2=x^3-5187x+129116$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[]$
486720.qj2	486720qj1	486720.qj	486720qj	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{6} \cdot 3^{9} \cdot 5^{4} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$1032192$	$1.081118$	$150568768/16875$	$0.91075$	$2.84644$	$[0, 0, 0, -5187, -129116]$	$y^2=x^3-5187x-129116$	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[]$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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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