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 (17 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
4830.h1	4830h1	4830.h	4830h	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{30} \cdot 3^{5} \cdot 5^{5} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$1$	$1$		$1$	$72000$	$2.148251$	$2625564132023811051529/918925030195200000$	$[1, 0, 1, -287409, 37259332]$	\(y^2+xy+y=x^3-287409x+37259332\)
14490.bu1	14490bv1	14490.bu	14490bv	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{30} \cdot 3^{11} \cdot 5^{5} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.204243302$	$1$		$17$	$576000$	$2.697556$	$2625564132023811051529/918925030195200000$	$[1, -1, 1, -2586677, -1006001971]$	\(y^2+xy+y=x^3-x^2-2586677x-1006001971\)
24150.bu1	24150bu1	24150.bu	24150bu	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{30} \cdot 3^{5} \cdot 5^{11} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$1728000$	$2.952969$	$2625564132023811051529/918925030195200000$	$[1, 1, 1, -7185213, 4657416531]$	\(y^2+xy+y=x^3+x^2-7185213x+4657416531\)
33810.u1	33810p1	33810.u	33810p	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{30} \cdot 3^{5} \cdot 5^{5} \cdot 7^{8} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4.931143068$	$1$		$3$	$3456000$	$3.121204$	$2625564132023811051529/918925030195200000$	$[1, 1, 0, -14083017, -12794033979]$	\(y^2+xy=x^3+x^2-14083017x-12794033979\)
38640.w1	38640bq1	38640.w	38640bq	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{42} \cdot 3^{5} \cdot 5^{5} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$9$	$3$	$1$	$1728000$	$2.841396$	$2625564132023811051529/918925030195200000$	$[0, -1, 0, -4598536, -2384597264]$	\(y^2=x^3-x^2-4598536x-2384597264\)
72450.bx1	72450bl1	72450.bx	72450bl	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{30} \cdot 3^{11} \cdot 5^{11} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$11.05259124$	$1$		$1$	$13824000$	$3.502274$	$2625564132023811051529/918925030195200000$	$[1, -1, 0, -64666917, -125814913259]$	\(y^2+xy=x^3-x^2-64666917x-125814913259\)
101430.dk1	101430eb1	101430.dk	101430eb	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{30} \cdot 3^{11} \cdot 5^{5} \cdot 7^{8} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3.015642810$	$1$		$5$	$27648000$	$3.670513$	$2625564132023811051529/918925030195200000$	$[1, -1, 1, -126747158, 345312170277]$	\(y^2+xy+y=x^3-x^2-126747158x+345312170277\)
111090.bj1	111090bg1	111090.bj	111090bg	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23^{2} \)	\( 2^{30} \cdot 3^{5} \cdot 5^{5} \cdot 7^{2} \cdot 23^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.609073297$	$1$		$7$	$38016000$	$3.715996$	$2625564132023811051529/918925030195200000$	$[1, 0, 1, -152039108, -453638373694]$	\(y^2+xy+y=x^3-152039108x-453638373694\)
115920.ep1	115920er1	115920.ep	115920er	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{42} \cdot 3^{11} \cdot 5^{5} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5.281353230$	$1$		$3$	$13824000$	$3.390705$	$2625564132023811051529/918925030195200000$	$[0, 0, 0, -41386827, 64425512954]$	\(y^2=x^3-41386827x+64425512954\)
154560.cr1	154560gz1	154560.cr	154560gz	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{48} \cdot 3^{5} \cdot 5^{5} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$13824000$	$3.187969$	$2625564132023811051529/918925030195200000$	$[0, -1, 0, -18394145, 19095172257]$	\(y^2=x^3-x^2-18394145x+19095172257\)
154560.hw1	154560e1	154560.hw	154560e	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{48} \cdot 3^{5} \cdot 5^{5} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$13824000$	$3.187969$	$2625564132023811051529/918925030195200000$	$[0, 1, 0, -18394145, -19095172257]$	\(y^2=x^3+x^2-18394145x-19095172257\)
169050.ia1	169050bi1	169050.ia	169050bi	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( 2^{30} \cdot 3^{5} \cdot 5^{11} \cdot 7^{8} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.695018282$	$1$		$11$	$82944000$	$3.925922$	$2625564132023811051529/918925030195200000$	$[1, 0, 0, -352075438, -1598550096508]$	\(y^2+xy=x^3-352075438x-1598550096508\)
193200.eo1	193200cf1	193200.eo	193200cf	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{42} \cdot 3^{5} \cdot 5^{11} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$9.941552086$	$1$		$1$	$41472000$	$3.646118$	$2625564132023811051529/918925030195200000$	$[0, 1, 0, -114963408, -298304584812]$	\(y^2=x^3+x^2-114963408x-298304584812\)
270480.io1	270480io1	270480.io	270480io	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{42} \cdot 3^{5} \cdot 5^{5} \cdot 7^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$82944000$	$3.814354$	$2625564132023811051529/918925030195200000$	$[0, 1, 0, -225328280, 818367518100]$	\(y^2=x^3+x^2-225328280x+818367518100\)
333270.dq1	333270dq1	333270.dq	333270dq	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23^{2} \)	\( 2^{30} \cdot 3^{11} \cdot 5^{5} \cdot 7^{2} \cdot 23^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3.083473029$	$1$		$5$	$304128000$	$4.265305$	$2625564132023811051529/918925030195200000$	$[1, -1, 1, -1368351968, 12248236089731]$	\(y^2+xy+y=x^3-x^2-1368351968x+12248236089731\)
463680.by1	463680by1	463680.by	463680by	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{48} \cdot 3^{11} \cdot 5^{5} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$45.31620283$	$1$		$1$	$110592000$	$3.737278$	$2625564132023811051529/918925030195200000$	$[0, 0, 0, -165547308, -515404103632]$	\(y^2=x^3-165547308x-515404103632\)
463680.ft1	463680ft1	463680.ft	463680ft	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{48} \cdot 3^{11} \cdot 5^{5} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$4$	$2$	$1$	$110592000$	$3.737278$	$2625564132023811051529/918925030195200000$	$[0, 0, 0, -165547308, 515404103632]$	\(y^2=x^3-165547308x+515404103632\)