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

Sort order

Select

Results (20 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
7098.k3	7098o1	7098.k	7098o	$4$	$10$	\( 2 \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{2} \cdot 3^{5} \cdot 7 \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$1$	$1$		$1$	$31200$	$1.560802$	$4649101309/6804$	$[1, 0, 1, -76392, -8122814]$	\(y^2+xy+y=x^3-76392x-8122814\)
7098.bc3	7098y1	7098.bc	7098y	$4$	$10$	\( 2 \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{2} \cdot 3^{5} \cdot 7 \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$1$	$1$		$1$	$2400$	$0.278327$	$4649101309/6804$	$[1, 0, 0, -452, -3732]$	\(y^2+xy=x^3-452x-3732\)
21294.f3	21294z1	21294.f	21294z	$4$	$10$	\( 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} \)	\( 2^{2} \cdot 3^{11} \cdot 7 \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$0.548635522$	$1$		$9$	$19200$	$0.827633$	$4649101309/6804$	$[1, -1, 0, -4068, 100764]$	\(y^2+xy=x^3-x^2-4068x+100764\)
21294.cp3	21294cv1	21294.cp	21294cv	$4$	$10$	\( 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} \)	\( 2^{2} \cdot 3^{11} \cdot 7 \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$6.550272042$	$1$		$1$	$249600$	$2.110107$	$4649101309/6804$	$[1, -1, 1, -687524, 219315971]$	\(y^2+xy+y=x^3-x^2-687524x+219315971\)
49686.s3	49686v1	49686.s	49686v	$4$	$10$	\( 2 \cdot 3 \cdot 7^{2} \cdot 13^{2} \)	\( 2^{2} \cdot 3^{5} \cdot 7^{7} \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$4.778856065$	$1$		$3$	$1497600$	$2.533756$	$4649101309/6804$	$[1, 1, 0, -3743184, 2782381932]$	\(y^2+xy=x^3+x^2-3743184x+2782381932\)
49686.bx3	49686cp1	49686.bx	49686cp	$4$	$10$	\( 2 \cdot 3 \cdot 7^{2} \cdot 13^{2} \)	\( 2^{2} \cdot 3^{5} \cdot 7^{7} \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$1$	$1$		$1$	$115200$	$1.251282$	$4649101309/6804$	$[1, 1, 1, -22149, 1257927]$	\(y^2+xy+y=x^3+x^2-22149x+1257927\)
56784.f3	56784bq1	56784.f	56784bq	$4$	$10$	\( 2^{4} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{14} \cdot 3^{5} \cdot 7 \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$6.111238709$	$1$		$1$	$748800$	$2.253948$	$4649101309/6804$	$[0, -1, 0, -1222264, 519860080]$	\(y^2=x^3-x^2-1222264x+519860080\)
56784.bj3	56784cg1	56784.bj	56784cg	$4$	$10$	\( 2^{4} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{14} \cdot 3^{5} \cdot 7 \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$1$	$1$		$1$	$57600$	$0.971474$	$4649101309/6804$	$[0, -1, 0, -7232, 238848]$	\(y^2=x^3-x^2-7232x+238848\)
149058.dh3	149058gh1	149058.dh	149058gh	$4$	$10$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \)	\( 2^{2} \cdot 3^{11} \cdot 7^{7} \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$1$	$1$		$1$	$921600$	$1.800589$	$4649101309/6804$	$[1, -1, 0, -199341, -34163375]$	\(y^2+xy=x^3-x^2-199341x-34163375\)
149058.fk3	149058s1	149058.fk	149058s	$4$	$10$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \)	\( 2^{2} \cdot 3^{11} \cdot 7^{7} \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$18.81101408$	$1$		$1$	$11980800$	$3.083061$	$4649101309/6804$	$[1, -1, 1, -33688661, -75158000823]$	\(y^2+xy+y=x^3-x^2-33688661x-75158000823\)
170352.bs3	170352q1	170352.bs	170352q	$4$	$10$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 13^{2} \)	\( 2^{14} \cdot 3^{11} \cdot 7 \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$4.936962750$	$1$		$3$	$460800$	$1.520781$	$4649101309/6804$	$[0, 0, 0, -65091, -6383806]$	\(y^2=x^3-65091x-6383806\)
170352.ev3	170352ci1	170352.ev	170352ci	$4$	$10$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 13^{2} \)	\( 2^{14} \cdot 3^{11} \cdot 7 \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$1$	$9$	$3$	$1$	$5990400$	$2.803253$	$4649101309/6804$	$[0, 0, 0, -11000379, -14025221782]$	\(y^2=x^3-11000379x-14025221782\)
177450.bw3	177450iw1	177450.bw	177450iw	$4$	$10$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} \)	\( 2^{2} \cdot 3^{5} \cdot 5^{6} \cdot 7 \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$4.831152972$	$1$		$3$	$307200$	$1.083046$	$4649101309/6804$	$[1, 1, 0, -11300, -466500]$	\(y^2+xy=x^3+x^2-11300x-466500\)
177450.fy3	177450ew1	177450.fy	177450ew	$4$	$10$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} \)	\( 2^{2} \cdot 3^{5} \cdot 5^{6} \cdot 7 \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$30.96598875$	$1$		$1$	$3993600$	$2.365520$	$4649101309/6804$	$[1, 1, 1, -1909788, -1015351719]$	\(y^2+xy+y=x^3+x^2-1909788x-1015351719\)
227136.v3	227136hq1	227136.v	227136hq	$4$	$10$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{20} \cdot 3^{5} \cdot 7 \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$1$	$1$		$1$	$460800$	$1.318048$	$4649101309/6804$	$[0, -1, 0, -28929, -1881855]$	\(y^2=x^3-x^2-28929x-1881855\)
227136.dx3	227136iu1	227136.dx	227136iu	$4$	$10$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{20} \cdot 3^{5} \cdot 7 \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$44.90324979$	$1$		$1$	$5990400$	$2.600521$	$4649101309/6804$	$[0, -1, 0, -4889057, -4153991583]$	\(y^2=x^3-x^2-4889057x-4153991583\)
227136.gb3	227136j1	227136.gb	227136j	$4$	$10$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{20} \cdot 3^{5} \cdot 7 \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$1.063457285$	$1$		$5$	$460800$	$1.318048$	$4649101309/6804$	$[0, 1, 0, -28929, 1881855]$	\(y^2=x^3+x^2-28929x+1881855\)
227136.ic3	227136bw1	227136.ic	227136bw	$4$	$10$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{20} \cdot 3^{5} \cdot 7 \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$1$	$1$		$1$	$5990400$	$2.600521$	$4649101309/6804$	$[0, 1, 0, -4889057, 4153991583]$	\(y^2=x^3+x^2-4889057x+4153991583\)
397488.gk3	397488gk1	397488.gk	397488gk	$4$	$10$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} \)	\( 2^{14} \cdot 3^{5} \cdot 7^{7} \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$0.963632862$	$1$		$7$	$2764800$	$1.944429$	$4649101309/6804$	$[0, 1, 0, -354384, -81216108]$	\(y^2=x^3+x^2-354384x-81216108\)
397488.jb3	397488jb1	397488.jb	397488jb	$4$	$10$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} \)	\( 2^{14} \cdot 3^{5} \cdot 7^{7} \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$10.55535843$	$1$		$1$	$35942400$	$3.226902$	$4649101309/6804$	$[0, 1, 0, -59890952, -178192225548]$	\(y^2=x^3+x^2-59890952x-178192225548\)