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 (26 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
2760.k2	2760j1	2760.k	2760j	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{10} \cdot 3^{5} \cdot 5 \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$10560$	$1.497843$	$-3552342505518244/179863605135$	$0.97850$	$5.40475$	$[0, 1, 0, -32040, 2291328]$	$y^2=x^3+x^2-32040x+2291328$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
5520.k2	5520d1	5520.k	5520d	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{10} \cdot 3^{5} \cdot 5 \cdot 23^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$3.281281916$	$1$		$3$	$21120$	$1.497843$	$-3552342505518244/179863605135$	$0.97850$	$4.96995$	$[0, -1, 0, -32040, -2291328]$	$y^2=x^3-x^2-32040x-2291328$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[(622, 14766)]$
8280.f2	8280g1	8280.f	8280g	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 $	$ - 2^{10} \cdot 3^{11} \cdot 5 \cdot 23^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$3.161327839$	$1$		$3$	$84480$	$2.047150$	$-3552342505518244/179863605135$	$0.97850$	$5.47723$	$[0, 0, 0, -288363, -62154218]$	$y^2=x^3-288363x-62154218$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[(51407, 11654928)]$
13800.i2	13800d1	13800.i	13800d	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 23 $	$ - 2^{10} \cdot 3^{5} \cdot 5^{7} \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$253440$	$2.302563$	$-3552342505518244/179863605135$	$0.97850$	$5.50525$	$[0, -1, 0, -801008, 288018012]$	$y^2=x^3-x^2-801008x+288018012$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
16560.l2	16560i1	16560.l	16560i	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 23 $	$ - 2^{10} \cdot 3^{11} \cdot 5 \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$168960$	$2.047150$	$-3552342505518244/179863605135$	$0.97850$	$5.08643$	$[0, 0, 0, -288363, 62154218]$	$y^2=x^3-288363x+62154218$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
22080.n2	22080c1	22080.n	22080c	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{16} \cdot 3^{5} \cdot 5 \cdot 23^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$4.687793425$	$1$		$5$	$168960$	$1.844418$	$-3552342505518244/179863605135$	$0.97850$	$4.69692$	$[0, -1, 0, -128161, 18458785]$	$y^2=x^3-x^2-128161x+18458785$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[(-399, 2432)]$
22080.bu2	22080cp1	22080.bu	22080cp	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{16} \cdot 3^{5} \cdot 5 \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$168960$	$1.844418$	$-3552342505518244/179863605135$	$0.97850$	$4.69692$	$[0, 1, 0, -128161, -18458785]$	$y^2=x^3+x^2-128161x-18458785$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
27600.co2	27600t1	27600.co	27600t	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 23 $	$ - 2^{10} \cdot 3^{5} \cdot 5^{7} \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$506880$	$2.302563$	$-3552342505518244/179863605135$	$0.97850$	$5.13207$	$[0, 1, 0, -801008, -288018012]$	$y^2=x^3+x^2-801008x-288018012$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
41400.bb2	41400bj1	41400.bb	41400bj	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ - 2^{10} \cdot 3^{11} \cdot 5^{7} \cdot 23^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$16.85562297$	$1$		$1$	$2027520$	$2.851868$	$-3552342505518244/179863605135$	$0.97850$	$5.55638$	$[0, 0, 0, -7209075, -7769277250]$	$y^2=x^3-7209075x-7769277250$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[(898439995/523, 9034769048400/523)]$
63480.m2	63480o1	63480.m	63480o	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23^{2} $	$ - 2^{10} \cdot 3^{5} \cdot 5 \cdot 23^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$5575680$	$3.065590$	$-3552342505518244/179863605135$	$0.97850$	$5.57352$	$[0, 1, 0, -16949336, -28014182016]$	$y^2=x^3+x^2-16949336x-28014182016$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
66240.ep2	66240fj1	66240.ep	66240fj	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 23 $	$ - 2^{16} \cdot 3^{11} \cdot 5 \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$1351680$	$2.393723$	$-3552342505518244/179863605135$	$0.97850$	$4.82588$	$[0, 0, 0, -1153452, 497233744]$	$y^2=x^3-1153452x+497233744$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
66240.eu2	66240ct1	66240.eu	66240ct	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 23 $	$ - 2^{16} \cdot 3^{11} \cdot 5 \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$1351680$	$2.393723$	$-3552342505518244/179863605135$	$0.97850$	$4.82588$	$[0, 0, 0, -1153452, -497233744]$	$y^2=x^3-1153452x-497233744$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
82800.dg2	82800be1	82800.dg	82800be	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ - 2^{10} \cdot 3^{11} \cdot 5^{7} \cdot 23^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$0.523487779$	$1$		$11$	$4055040$	$2.851868$	$-3552342505518244/179863605135$	$0.97850$	$5.21627$	$[0, 0, 0, -7209075, 7769277250]$	$y^2=x^3-7209075x+7769277250$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[(59, 85698)]$
110400.cv2	110400fj1	110400.cv	110400fj	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 23 $	$ - 2^{16} \cdot 3^{5} \cdot 5^{7} \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$4$	$2$	$1$	$4055040$	$2.649136$	$-3552342505518244/179863605135$	$0.97850$	$4.87753$	$[0, -1, 0, -3204033, -2300940063]$	$y^2=x^3-x^2-3204033x-2300940063$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
110400.gy2	110400do1	110400.gy	110400do	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 23 $	$ - 2^{16} \cdot 3^{5} \cdot 5^{7} \cdot 23^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$0.335004081$	$1$		$9$	$4055040$	$2.649136$	$-3552342505518244/179863605135$	$0.97850$	$4.87753$	$[0, 1, 0, -3204033, 2300940063]$	$y^2=x^3+x^2-3204033x+2300940063$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[(-237, 55200)]$
126960.o2	126960a1	126960.o	126960a	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 23^{2} $	$ - 2^{10} \cdot 3^{5} \cdot 5 \cdot 23^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$4$	$2$	$1$	$11151360$	$3.065590$	$-3552342505518244/179863605135$	$0.97850$	$5.24478$	$[0, -1, 0, -16949336, 28014182016]$	$y^2=x^3-x^2-16949336x+28014182016$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
135240.k2	135240bw1	135240.k	135240bw	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 $	$ - 2^{10} \cdot 3^{5} \cdot 5 \cdot 7^{6} \cdot 23^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$30.63592152$	$1$		$1$	$4055040$	$2.470798$	$-3552342505518244/179863605135$	$0.97850$	$4.61262$	$[0, -1, 0, -1569976, -789065444]$	$y^2=x^3-x^2-1569976x-789065444$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[(133284081513537/104828, 1530109058149316815303/104828)]$
190440.bn2	190440bd1	190440.bn	190440bd	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 23^{2} $	$ - 2^{10} \cdot 3^{11} \cdot 5 \cdot 23^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$4$	$2$	$1$	$44605440$	$3.614899$	$-3552342505518244/179863605135$	$0.97850$	$5.61206$	$[0, 0, 0, -152544027, 756230370406]$	$y^2=x^3-152544027x+756230370406$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
270480.fo2	270480fo1	270480.fo	270480fo	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 $	$ - 2^{10} \cdot 3^{5} \cdot 5 \cdot 7^{6} \cdot 23^{6} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1.312776355$	$1$		$21$	$8110080$	$2.470798$	$-3552342505518244/179863605135$	$0.97850$	$4.35700$	$[0, 1, 0, -1569976, 789065444]$	$y^2=x^3+x^2-1569976x+789065444$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[(800, 6762), (-304, 35190)]$
317400.n2	317400n1	317400.n	317400n	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 23^{2} $	$ - 2^{10} \cdot 3^{5} \cdot 5^{7} \cdot 23^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$133816320$	$3.870308$	$-3552342505518244/179863605135$	$0.97850$	$5.62771$	$[0, -1, 0, -423733408, -3500925285188]$	$y^2=x^3-x^2-423733408x-3500925285188$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
331200.ic2	331200ic1	331200.ic	331200ic	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ - 2^{16} \cdot 3^{11} \cdot 5^{7} \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$32440320$	$3.198441$	$-3552342505518244/179863605135$	$0.97850$	$4.97455$	$[0, 0, 0, -28836300, 62154218000]$	$y^2=x^3-28836300x+62154218000$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
331200.ja2	331200ja1	331200.ja	331200ja	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 23 $	$ - 2^{16} \cdot 3^{11} \cdot 5^{7} \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$32440320$	$3.198441$	$-3552342505518244/179863605135$	$0.97850$	$4.97455$	$[0, 0, 0, -28836300, -62154218000]$	$y^2=x^3-28836300x-62154218000$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
333960.dc2	333960dc1	333960.dc	333960dc	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 23 $	$ - 2^{10} \cdot 3^{5} \cdot 5 \cdot 11^{6} \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$14784000$	$2.696793$	$-3552342505518244/179863605135$	$0.97850$	$4.49800$	$[0, 1, 0, -3876880, -3065265040]$	$y^2=x^3+x^2-3876880x-3065265040$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
380880.fe2	380880fe1	380880.fe	380880fe	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 23^{2} $	$ - 2^{10} \cdot 3^{11} \cdot 5 \cdot 23^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$25$	$5$	$1$	$89210880$	$3.614899$	$-3552342505518244/179863605135$	$0.97850$	$5.30935$	$[0, 0, 0, -152544027, -756230370406]$	$y^2=x^3-152544027x-756230370406$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
405720.eq2	405720eq1	405720.eq	405720eq	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 $	$ - 2^{10} \cdot 3^{11} \cdot 5 \cdot 7^{6} \cdot 23^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$6.570683180$	$1$		$1$	$32440320$	$3.020103$	$-3552342505518244/179863605135$	$0.97850$	$4.73065$	$[0, 0, 0, -14129787, 21318896774]$	$y^2=x^3-14129787x+21318896774$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[(7855/3, 2652544/3)]$
466440.bl2	466440bl1	466440.bl	466440bl	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 13^{2} \cdot 23 $	$ - 2^{10} \cdot 3^{5} \cdot 5 \cdot 13^{6} \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$24837120$	$2.780319$	$-3552342505518244/179863605135$	$0.97850$	$4.45966$	$[0, 1, 0, -5414816, 5055706800]$	$y^2=x^3+x^2-5414816x+5055706800$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$

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Elliptic 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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