Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (26 matches)

 

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
2760.k1	2760j2	2760.k	2760j	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{2} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$21120$	$1.844418$	$7536914291382802562/17961229575$	$[0, 1, 0, -518720, 143623200]$	\(y^2=x^3+x^2-518720x+143623200\)
5520.k1	5520d2	5520.k	5520d	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{2} \cdot 23^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.640640958$	$1$		$3$	$42240$	$1.844418$	$7536914291382802562/17961229575$	$[0, -1, 0, -518720, -143623200]$	\(y^2=x^3-x^2-518720x-143623200\)
8280.f1	8280g2	8280.f	8280g	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)	\( 2^{11} \cdot 3^{16} \cdot 5^{2} \cdot 23^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6.322655678$	$1$		$1$	$168960$	$2.393723$	$7536914291382802562/17961229575$	$[0, 0, 0, -4668483, -3882494882]$	\(y^2=x^3-4668483x-3882494882\)
13800.i1	13800d2	13800.i	13800d	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{8} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$506880$	$2.649136$	$7536914291382802562/17961229575$	$[0, -1, 0, -12968008, 17978836012]$	\(y^2=x^3-x^2-12968008x+17978836012\)
16560.l1	16560i2	16560.l	16560i	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 23 \)	\( 2^{11} \cdot 3^{16} \cdot 5^{2} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$337920$	$2.393723$	$7536914291382802562/17961229575$	$[0, 0, 0, -4668483, 3882494882]$	\(y^2=x^3-4668483x+3882494882\)
22080.n1	22080c2	22080.n	22080c	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 23 \)	\( 2^{17} \cdot 3^{10} \cdot 5^{2} \cdot 23^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.343896712$	$1$		$7$	$337920$	$2.190990$	$7536914291382802562/17961229575$	$[0, -1, 0, -2074881, 1151060481]$	\(y^2=x^3-x^2-2074881x+1151060481\)
22080.bu1	22080cp2	22080.bu	22080cp	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 23 \)	\( 2^{17} \cdot 3^{10} \cdot 5^{2} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$337920$	$2.190990$	$7536914291382802562/17961229575$	$[0, 1, 0, -2074881, -1151060481]$	\(y^2=x^3+x^2-2074881x-1151060481\)
27600.co1	27600t2	27600.co	27600t	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{8} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$1013760$	$2.649136$	$7536914291382802562/17961229575$	$[0, 1, 0, -12968008, -17978836012]$	\(y^2=x^3+x^2-12968008x-17978836012\)
41400.bb1	41400bj2	41400.bb	41400bj	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{16} \cdot 5^{8} \cdot 23^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$33.71124595$	$1$		$1$	$4055040$	$3.198441$	$7536914291382802562/17961229575$	$[0, 0, 0, -116712075, -485311860250]$	\(y^2=x^3-116712075x-485311860250\)
63480.m1	63480o2	63480.m	63480o	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 23^{2} \)	\( 2^{11} \cdot 3^{10} \cdot 5^{2} \cdot 23^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$11151360$	$3.412163$	$7536914291382802562/17961229575$	$[0, 1, 0, -274403056, -1749658698400]$	\(y^2=x^3+x^2-274403056x-1749658698400\)
66240.ep1	66240fj2	66240.ep	66240fj	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 23 \)	\( 2^{17} \cdot 3^{16} \cdot 5^{2} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$2703360$	$2.740295$	$7536914291382802562/17961229575$	$[0, 0, 0, -18673932, 31059959056]$	\(y^2=x^3-18673932x+31059959056\)
66240.eu1	66240ct2	66240.eu	66240ct	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 23 \)	\( 2^{17} \cdot 3^{16} \cdot 5^{2} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$2703360$	$2.740295$	$7536914291382802562/17961229575$	$[0, 0, 0, -18673932, -31059959056]$	\(y^2=x^3-18673932x-31059959056\)
82800.dg1	82800be2	82800.dg	82800be	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{16} \cdot 5^{8} \cdot 23^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.046975558$	$1$		$7$	$8110080$	$3.198441$	$7536914291382802562/17961229575$	$[0, 0, 0, -116712075, 485311860250]$	\(y^2=x^3-116712075x+485311860250\)
110400.cv1	110400fj2	110400.cv	110400fj	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 23 \)	\( 2^{17} \cdot 3^{10} \cdot 5^{8} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$4$	$2$	$1$	$8110080$	$2.995708$	$7536914291382802562/17961229575$	$[0, -1, 0, -51872033, -143778816063]$	\(y^2=x^3-x^2-51872033x-143778816063\)
110400.gy1	110400do2	110400.gy	110400do	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 23 \)	\( 2^{17} \cdot 3^{10} \cdot 5^{8} \cdot 23^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.670008162$	$1$		$9$	$8110080$	$2.995708$	$7536914291382802562/17961229575$	$[0, 1, 0, -51872033, 143778816063]$	\(y^2=x^3+x^2-51872033x+143778816063\)
126960.o1	126960a2	126960.o	126960a	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 23^{2} \)	\( 2^{11} \cdot 3^{10} \cdot 5^{2} \cdot 23^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$22302720$	$3.412163$	$7536914291382802562/17961229575$	$[0, -1, 0, -274403056, 1749658698400]$	\(y^2=x^3-x^2-274403056x+1749658698400\)
135240.k1	135240bw2	135240.k	135240bw	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{2} \cdot 7^{6} \cdot 23^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$15.31796076$	$1$		$1$	$8110080$	$2.817371$	$7536914291382802562/17961229575$	$[0, -1, 0, -25417296, -49313592180]$	\(y^2=x^3-x^2-25417296x-49313592180\)
190440.bn1	190440bd2	190440.bn	190440bd	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 23^{2} \)	\( 2^{11} \cdot 3^{16} \cdot 5^{2} \cdot 23^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$4$	$2$	$1$	$89210880$	$3.961472$	$7536914291382802562/17961229575$	$[0, 0, 0, -2469627507, 47238315229294]$	\(y^2=x^3-2469627507x+47238315229294\)
270480.fo1	270480fo2	270480.fo	270480fo	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{2} \cdot 7^{6} \cdot 23^{3} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.328194088$	$1$		$39$	$16220160$	$2.817371$	$7536914291382802562/17961229575$	$[0, 1, 0, -25417296, 49313592180]$	\(y^2=x^3+x^2-25417296x+49313592180\)
317400.n1	317400n2	317400.n	317400n	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 23^{2} \)	\( 2^{11} \cdot 3^{10} \cdot 5^{8} \cdot 23^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$267632640$	$4.216881$	$7536914291382802562/17961229575$	$[0, -1, 0, -6860076408, -218693617147188]$	\(y^2=x^3-x^2-6860076408x-218693617147188\)
331200.ic1	331200ic2	331200.ic	331200ic	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 23 \)	\( 2^{17} \cdot 3^{16} \cdot 5^{8} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$64880640$	$3.545017$	$7536914291382802562/17961229575$	$[0, 0, 0, -466848300, 3882494882000]$	\(y^2=x^3-466848300x+3882494882000\)
331200.ja1	331200ja2	331200.ja	331200ja	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 23 \)	\( 2^{17} \cdot 3^{16} \cdot 5^{8} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$64880640$	$3.545017$	$7536914291382802562/17961229575$	$[0, 0, 0, -466848300, -3882494882000]$	\(y^2=x^3-466848300x-3882494882000\)
333960.dc1	333960dc2	333960.dc	333960dc	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{2} \cdot 11^{6} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$29568000$	$3.043365$	$7536914291382802562/17961229575$	$[0, 1, 0, -62765160, -191413539792]$	\(y^2=x^3+x^2-62765160x-191413539792\)
380880.fe1	380880fe2	380880.fe	380880fe	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 23^{2} \)	\( 2^{11} \cdot 3^{16} \cdot 5^{2} \cdot 23^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$25$	$5$	$1$	$178421760$	$3.961472$	$7536914291382802562/17961229575$	$[0, 0, 0, -2469627507, -47238315229294]$	\(y^2=x^3-2469627507x-47238315229294\)
405720.eq1	405720eq2	405720.eq	405720eq	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{16} \cdot 5^{2} \cdot 7^{6} \cdot 23^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3.285341590$	$1$		$3$	$64880640$	$3.366680$	$7536914291382802562/17961229575$	$[0, 0, 0, -228755667, 1331695744526]$	\(y^2=x^3-228755667x+1331695744526\)
466440.bl1	466440bl2	466440.bl	466440bl	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 13^{2} \cdot 23 \)	\( 2^{11} \cdot 3^{10} \cdot 5^{2} \cdot 13^{6} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$49674240$	$3.126892$	$7536914291382802562/17961229575$	$[0, 1, 0, -87663736, 315890825264]$	\(y^2=x^3+x^2-87663736x+315890825264\)