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 (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
11550.f4	11550n1	11550.f	11550n	$4$	$10$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{4} \cdot 3^{2} \cdot 5^{9} \cdot 7 \cdot 11^{5} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.24.0.4	2B, 5B.1.3	$2.283138390$	$1$		$3$	$192000$	$2.206429$	$1433528304665250149/162339408$	$[1, 1, 0, -2936325, -1937887875]$	\(y^2+xy=x^3+x^2-2936325x-1937887875\)
11550.cu4	11550cu1	11550.cu	11550cu	$4$	$10$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{4} \cdot 3^{2} \cdot 5^{3} \cdot 7 \cdot 11^{5} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.24.0.3	2B, 5B.1.2	$1$	$1$		$1$	$38400$	$1.401711$	$1433528304665250149/162339408$	$[1, 0, 0, -117453, -15503103]$	\(y^2+xy=x^3-117453x-15503103\)
34650.bp4	34650cb1	34650.bp	34650cb	$4$	$10$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{4} \cdot 3^{8} \cdot 5^{3} \cdot 7 \cdot 11^{5} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$1$	$1$		$1$	$307200$	$1.951015$	$1433528304665250149/162339408$	$[1, -1, 0, -1057077, 418583781]$	\(y^2+xy=x^3-x^2-1057077x+418583781\)
34650.cl4	34650dx1	34650.cl	34650dx	$4$	$10$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{4} \cdot 3^{8} \cdot 5^{9} \cdot 7 \cdot 11^{5} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$1$	$1$		$1$	$1536000$	$2.755733$	$1433528304665250149/162339408$	$[1, -1, 1, -26426930, 52296545697]$	\(y^2+xy+y=x^3-x^2-26426930x+52296545697\)
80850.de4	80850df1	80850.de	80850df	$4$	$10$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{4} \cdot 3^{2} \cdot 5^{9} \cdot 7^{7} \cdot 11^{5} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$1.031288376$	$1$		$5$	$9216000$	$3.179382$	$1433528304665250149/162339408$	$[1, 0, 1, -143879951, 664263901298]$	\(y^2+xy+y=x^3-143879951x+664263901298\)
80850.el4	80850fh1	80850.el	80850fh	$4$	$10$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{4} \cdot 3^{2} \cdot 5^{3} \cdot 7^{7} \cdot 11^{5} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$0.569374704$	$1$		$9$	$1843200$	$2.374664$	$1433528304665250149/162339408$	$[1, 1, 1, -5755198, 5311809131]$	\(y^2+xy+y=x^3+x^2-5755198x+5311809131\)
92400.t4	92400ez1	92400.t	92400ez	$4$	$10$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{16} \cdot 3^{2} \cdot 5^{3} \cdot 7 \cdot 11^{5} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$2.906092815$	$1$		$5$	$921600$	$2.094856$	$1433528304665250149/162339408$	$[0, -1, 0, -1879248, 992198592]$	\(y^2=x^3-x^2-1879248x+992198592\)
92400.gs4	92400ig1	92400.gs	92400ig	$4$	$10$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{16} \cdot 3^{2} \cdot 5^{9} \cdot 7 \cdot 11^{5} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$9.480281760$	$1$		$1$	$4608000$	$2.899574$	$1433528304665250149/162339408$	$[0, 1, 0, -46981208, 123930861588]$	\(y^2=x^3+x^2-46981208x+123930861588\)
127050.cm4	127050ea1	127050.cm	127050ea	$4$	$10$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{4} \cdot 3^{2} \cdot 5^{3} \cdot 7 \cdot 11^{11} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$1$	$1$		$1$	$4608000$	$2.600658$	$1433528304665250149/162339408$	$[1, 0, 1, -14211816, 20620418278]$	\(y^2+xy+y=x^3-14211816x+20620418278\)
127050.gx4	127050gy1	127050.gx	127050gy	$4$	$10$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{4} \cdot 3^{2} \cdot 5^{9} \cdot 7 \cdot 11^{11} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$10.48560724$	$1$		$1$	$23040000$	$3.405376$	$1433528304665250149/162339408$	$[1, 1, 1, -355295388, 2577552284781]$	\(y^2+xy+y=x^3+x^2-355295388x+2577552284781\)
242550.p4	242550p1	242550.p	242550p	$4$	$10$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{4} \cdot 3^{8} \cdot 5^{3} \cdot 7^{7} \cdot 11^{5} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$1$	$4$	$2$	$1$	$14745600$	$2.923969$	$1433528304665250149/162339408$	$[1, -1, 0, -51796782, -143470643324]$	\(y^2+xy=x^3-x^2-51796782x-143470643324\)
242550.kt4	242550kt1	242550.kt	242550kt	$4$	$10$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{4} \cdot 3^{8} \cdot 5^{9} \cdot 7^{7} \cdot 11^{5} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$15.48433410$	$1$		$1$	$73728000$	$3.728691$	$1433528304665250149/162339408$	$[1, -1, 1, -1294919555, -17935125335053]$	\(y^2+xy+y=x^3-x^2-1294919555x-17935125335053\)
277200.gg4	277200gg1	277200.gg	277200gg	$4$	$10$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{16} \cdot 3^{8} \cdot 5^{3} \cdot 7 \cdot 11^{5} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$2.779235410$	$1$		$3$	$7372800$	$2.644161$	$1433528304665250149/162339408$	$[0, 0, 0, -16913235, -26772448750]$	\(y^2=x^3-16913235x-26772448750\)
277200.lk4	277200lk1	277200.lk	277200lk	$4$	$10$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{16} \cdot 3^{8} \cdot 5^{9} \cdot 7 \cdot 11^{5} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$1$	$1$		$1$	$36864000$	$3.448883$	$1433528304665250149/162339408$	$[0, 0, 0, -422830875, -3346556093750]$	\(y^2=x^3-422830875x-3346556093750\)
369600.hd4	369600hd1	369600.hd	369600hd	$4$	$10$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{22} \cdot 3^{2} \cdot 5^{3} \cdot 7 \cdot 11^{5} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$13.63806388$	$1$		$1$	$7372800$	$2.441429$	$1433528304665250149/162339408$	$[0, -1, 0, -7516993, -7930071743]$	\(y^2=x^3-x^2-7516993x-7930071743\)
369600.ll4	369600ll1	369600.ll	369600ll	$4$	$10$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{22} \cdot 3^{2} \cdot 5^{9} \cdot 7 \cdot 11^{5} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$2.648779906$	$1$		$5$	$36864000$	$3.246151$	$1433528304665250149/162339408$	$[0, -1, 0, -187924833, 991634817537]$	\(y^2=x^3-x^2-187924833x+991634817537\)
369600.ny4	369600ny1	369600.ny	369600ny	$4$	$10$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{22} \cdot 3^{2} \cdot 5^{9} \cdot 7 \cdot 11^{5} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$71.96236746$	$1$		$1$	$36864000$	$3.246151$	$1433528304665250149/162339408$	$[0, 1, 0, -187924833, -991634817537]$	\(y^2=x^3+x^2-187924833x-991634817537\)
369600.ov4	369600ov1	369600.ov	369600ov	$4$	$10$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{22} \cdot 3^{2} \cdot 5^{3} \cdot 7 \cdot 11^{5} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$1.360202742$	$1$		$5$	$7372800$	$2.441429$	$1433528304665250149/162339408$	$[0, 1, 0, -7516993, 7930071743]$	\(y^2=x^3+x^2-7516993x+7930071743\)
381150.hr4	381150hr1	381150.hr	381150hr	$4$	$10$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{4} \cdot 3^{8} \cdot 5^{9} \cdot 7 \cdot 11^{11} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$20.99170006$	$1$		$1$	$184320000$	$3.954681$	$1433528304665250149/162339408$	$[1, -1, 0, -3197658492, -69597109347584]$	\(y^2+xy=x^3-x^2-3197658492x-69597109347584\)
381150.je4	381150je1	381150.je	381150je	$4$	$10$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{4} \cdot 3^{8} \cdot 5^{3} \cdot 7 \cdot 11^{11} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.12.0.2	2B, 5B.4.2	$8.248056790$	$1$		$1$	$36864000$	$3.149963$	$1433528304665250149/162339408$	$[1, -1, 1, -127906340, -556751293513]$	\(y^2+xy+y=x^3-x^2-127906340x-556751293513\)