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
20280.a2	20280r1	20280.a	20280r	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{10} \cdot 3^{5} \cdot 5^{6} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$14.53236180$	$1$		$1$	$748800$	$2.452572$	$-1735192372/3796875$	$0.97338$	$5.32953$	$[0, -1, 0, -554376, -347207940]$	$y^2=x^3-x^2-554376x-347207940$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(64677902/13, 520154662000/13)]$
20280.r2	20280j1	20280.r	20280j	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{10} \cdot 3^{5} \cdot 5^{6} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$3.228496746$	$1$		$3$	$57600$	$1.170099$	$-1735192372/3796875$	$0.97338$	$3.77775$	$[0, -1, 0, -3280, -157028]$	$y^2=x^3-x^2-3280x-157028$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(234, 3440)]$
40560.cf2	40560x1	40560.cf	40560x	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{10} \cdot 3^{5} \cdot 5^{6} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.211967311$	$1$		$5$	$1497600$	$2.452572$	$-1735192372/3796875$	$0.97338$	$4.98138$	$[0, 1, 0, -554376, 347207940]$	$y^2=x^3+x^2-554376x+347207940$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(42, 18000)]$
40560.cj2	40560bf1	40560.cj	40560bf	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{10} \cdot 3^{5} \cdot 5^{6} \cdot 13^{3} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$0.255969360$	$1$		$39$	$115200$	$1.170099$	$-1735192372/3796875$	$0.97338$	$3.53096$	$[0, 1, 0, -3280, 157028]$	$y^2=x^3+x^2-3280x+157028$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(56, 390), (-22, 468)]$
60840.y2	60840bp1	60840.y	60840bp	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{10} \cdot 3^{11} \cdot 5^{6} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$		$1$	$460800$	$1.719404$	$-1735192372/3796875$	$0.97338$	$3.99937$	$[0, 0, 0, -29523, 4269278]$	$y^2=x^3-29523x+4269278$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
60840.bc2	60840bd1	60840.bc	60840bd	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{10} \cdot 3^{11} \cdot 5^{6} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$		$1$	$5990400$	$3.001881$	$-1735192372/3796875$	$0.97338$	$5.39640$	$[0, 0, 0, -4989387, 9379603766]$	$y^2=x^3-4989387x+9379603766$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
101400.bz2	101400do1	101400.bz	101400do	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{10} \cdot 3^{5} \cdot 5^{12} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$		$1$	$1382400$	$1.974817$	$-1735192372/3796875$	$0.97338$	$4.08803$	$[0, 1, 0, -82008, -19792512]$	$y^2=x^3+x^2-82008x-19792512$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
101400.dp2	101400br1	101400.dp	101400br	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{10} \cdot 3^{5} \cdot 5^{12} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$13.48540433$	$1$		$1$	$17971200$	$3.257294$	$-1735192372/3796875$	$0.97338$	$5.42315$	$[0, 1, 0, -13859408, -43428711312]$	$y^2=x^3+x^2-13859408x-43428711312$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(26281972/67, 82997442000/67)]$
121680.i2	121680be1	121680.i	121680be	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{10} \cdot 3^{11} \cdot 5^{6} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$4.921101327$	$1$		$3$	$921600$	$1.719404$	$-1735192372/3796875$	$0.97338$	$3.76262$	$[0, 0, 0, -29523, -4269278]$	$y^2=x^3-29523x-4269278$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(4221, 274000)]$
121680.fp2	121680cc1	121680.fp	121680cc	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{10} \cdot 3^{11} \cdot 5^{6} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$4$	$2$	$1$	$11980800$	$3.001881$	$-1735192372/3796875$	$0.97338$	$5.07695$	$[0, 0, 0, -4989387, -9379603766]$	$y^2=x^3-4989387x-9379603766$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
162240.g2	162240di1	162240.g	162240di	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{16} \cdot 3^{5} \cdot 5^{6} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.037689145$	$1$		$5$	$921600$	$1.516672$	$-1735192372/3796875$	$0.97338$	$3.46960$	$[0, -1, 0, -13121, 1269345]$	$y^2=x^3-x^2-13121x+1269345$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(61, 832)]$
162240.dz2	162240dd1	162240.dz	162240dd	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{16} \cdot 3^{5} \cdot 5^{6} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$		$1$	$11980800$	$2.799149$	$-1735192372/3796875$	$0.97338$	$4.75242$	$[0, -1, 0, -2217505, 2779881025]$	$y^2=x^3-x^2-2217505x+2779881025$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
162240.fy2	162240go1	162240.fy	162240go	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{16} \cdot 3^{5} \cdot 5^{6} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$2.179612088$	$1$		$5$	$921600$	$1.516672$	$-1735192372/3796875$	$0.97338$	$3.46960$	$[0, 1, 0, -13121, -1269345]$	$y^2=x^3+x^2-13121x-1269345$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(355, 6240)]$
162240.gk2	162240en1	162240.gk	162240en	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{16} \cdot 3^{5} \cdot 5^{6} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$		$1$	$11980800$	$2.799149$	$-1735192372/3796875$	$0.97338$	$4.75242$	$[0, 1, 0, -2217505, -2779881025]$	$y^2=x^3+x^2-2217505x-2779881025$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
202800.p2	202800jd1	202800.p	202800jd	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{10} \cdot 3^{5} \cdot 5^{12} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$4$	$2$	$1$	$35942400$	$3.257294$	$-1735192372/3796875$	$0.97338$	$5.11553$	$[0, -1, 0, -13859408, 43428711312]$	$y^2=x^3-x^2-13859408x+43428711312$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
202800.fg2	202800kk1	202800.fg	202800kk	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{10} \cdot 3^{5} \cdot 5^{12} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$		$1$	$2764800$	$1.974817$	$-1735192372/3796875$	$0.97338$	$3.85615$	$[0, -1, 0, -82008, 19792512]$	$y^2=x^3-x^2-82008x+19792512$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
304200.d2	304200d1	304200.d	304200d	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{10} \cdot 3^{11} \cdot 5^{12} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$3.322468465$	$1$		$3$	$11059200$	$2.524124$	$-1735192372/3796875$	$0.97338$	$4.25440$	$[0, 0, 0, -738075, 533659750]$	$y^2=x^3-738075x+533659750$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(335, 18000)]$
304200.fv2	304200fv1	304200.fv	304200fv	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{10} \cdot 3^{11} \cdot 5^{12} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$9$	$3$	$1$	$143769600$	$3.806599$	$-1735192372/3796875$	$0.97338$	$5.47334$	$[0, 0, 0, -124734675, 1172450470750]$	$y^2=x^3-124734675x+1172450470750$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
486720.n2	486720n1	486720.n	486720n	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{16} \cdot 3^{11} \cdot 5^{6} \cdot 13^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$4.776176563$	$1$		$5$	$95846400$	$3.348454$	$-1735192372/3796875$	$0.97338$	$4.85708$	$[0, 0, 0, -19957548, 75036830128]$	$y^2=x^3-19957548x+75036830128$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(-3496, 319500)]$
486720.id2	486720id1	486720.id	486720id	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{16} \cdot 3^{11} \cdot 5^{6} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$9$	$3$	$1$	$95846400$	$3.348454$	$-1735192372/3796875$	$0.97338$	$4.85708$	$[0, 0, 0, -19957548, -75036830128]$	$y^2=x^3-19957548x-75036830128$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[]$
486720.iz2	486720iz1	486720.iz	486720iz	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{16} \cdot 3^{11} \cdot 5^{6} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1.186952048$	$1$		$7$	$7372800$	$2.065979$	$-1735192372/3796875$	$0.97338$	$3.68189$	$[0, 0, 0, -118092, -34154224]$	$y^2=x^3-118092x-34154224$	2.3.0.a.1, 78.6.0.?, 120.6.0.?, 520.6.0.?, 1560.12.0.?	$[(832, 21060)]$
486720.qp2	486720qp1	486720.qp	486720qp	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{16} \cdot 3^{11} \cdot 5^{6} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$		$1$	$7372800$	$2.065979$	$-1735192372/3796875$	$0.97338$	$3.68189$	$[0, 0, 0, -118092, 34154224]$	$y^2=x^3-118092x+34154224$	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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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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