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 (16 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
7245.e1	7245c1	7245.e	7245c	$2$	$2$	\( 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 3^{9} \cdot 5^{5} \cdot 7^{6} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$25920$	$1.506739$	$292583028222603/8456021875$	$[1, -1, 1, -37343, 2716606]$	\(y^2+xy+y=x^3-x^2-37343x+2716606\)
7245.r1	7245f1	7245.r	7245f	$2$	$2$	\( 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 3^{3} \cdot 5^{5} \cdot 7^{6} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$8640$	$0.957433$	$292583028222603/8456021875$	$[1, -1, 0, -4149, -99232]$	\(y^2+xy=x^3-x^2-4149x-99232\)
36225.z1	36225k1	36225.z	36225k	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 3^{3} \cdot 5^{11} \cdot 7^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.083883398$	$1$		$3$	$207360$	$1.762152$	$292583028222603/8456021875$	$[1, -1, 1, -103730, -12507728]$	\(y^2+xy+y=x^3-x^2-103730x-12507728\)
36225.bq1	36225d1	36225.bq	36225d	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 3^{9} \cdot 5^{11} \cdot 7^{6} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$622080$	$2.311459$	$292583028222603/8456021875$	$[1, -1, 0, -933567, 338642216]$	\(y^2+xy=x^3-x^2-933567x+338642216\)
50715.r1	50715g1	50715.r	50715g	$2$	$2$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 3^{9} \cdot 5^{5} \cdot 7^{12} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$1244160$	$2.479694$	$292583028222603/8456021875$	$[1, -1, 1, -1829792, -928136366]$	\(y^2+xy+y=x^3-x^2-1829792x-928136366\)
50715.bm1	50715b1	50715.bm	50715b	$2$	$2$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 3^{3} \cdot 5^{5} \cdot 7^{12} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$414720$	$1.930387$	$292583028222603/8456021875$	$[1, -1, 0, -203310, 34443191]$	\(y^2+xy=x^3-x^2-203310x+34443191\)
115920.ce1	115920cg1	115920.ce	115920cg	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{12} \cdot 3^{9} \cdot 5^{5} \cdot 7^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3.643738850$	$1$		$5$	$1658880$	$2.199886$	$292583028222603/8456021875$	$[0, 0, 0, -597483, -173265318]$	\(y^2=x^3-597483x-173265318\)
115920.ee1	115920cs1	115920.ee	115920cs	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{12} \cdot 3^{3} \cdot 5^{5} \cdot 7^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.279180676$	$1$		$13$	$552960$	$1.650579$	$292583028222603/8456021875$	$[0, 0, 0, -66387, 6417234]$	\(y^2=x^3-66387x+6417234\)
166635.q1	166635q1	166635.q	166635q	$2$	$2$	\( 3^{2} \cdot 5 \cdot 7 \cdot 23^{2} \)	\( 3^{9} \cdot 5^{5} \cdot 7^{6} \cdot 23^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$13685760$	$3.074486$	$292583028222603/8456021875$	$[1, -1, 1, -19754282, -32934422744]$	\(y^2+xy+y=x^3-x^2-19754282x-32934422744\)
166635.bl1	166635bx1	166635.bl	166635bx	$2$	$2$	\( 3^{2} \cdot 5 \cdot 7 \cdot 23^{2} \)	\( 3^{3} \cdot 5^{5} \cdot 7^{6} \cdot 23^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.270229508$	$1$		$3$	$4561920$	$2.525181$	$292583028222603/8456021875$	$[1, -1, 0, -2194920, 1220525075]$	\(y^2+xy=x^3-x^2-2194920x+1220525075\)
253575.ce1	253575ce1	253575.ce	253575ce	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( 3^{3} \cdot 5^{11} \cdot 7^{12} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8.945255954$	$1$		$1$	$9953280$	$2.735107$	$292583028222603/8456021875$	$[1, -1, 1, -5082755, 4300316122]$	\(y^2+xy+y=x^3-x^2-5082755x+4300316122\)
253575.ef1	253575ef1	253575.ef	253575ef	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( 3^{9} \cdot 5^{11} \cdot 7^{12} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$4$	$2$	$1$	$29859840$	$3.284412$	$292583028222603/8456021875$	$[1, -1, 0, -45744792, -116062790509]$	\(y^2+xy=x^3-x^2-45744792x-116062790509\)
463680.j1	463680j1	463680.j	463680j	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{18} \cdot 3^{3} \cdot 5^{5} \cdot 7^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5.715901354$	$1$		$3$	$4423680$	$1.997152$	$292583028222603/8456021875$	$[0, 0, 0, -265548, -51337872]$	\(y^2=x^3-265548x-51337872\)
463680.gq1	463680gq1	463680.gq	463680gq	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{18} \cdot 3^{3} \cdot 5^{5} \cdot 7^{6} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$4423680$	$1.997152$	$292583028222603/8456021875$	$[0, 0, 0, -265548, 51337872]$	\(y^2=x^3-265548x+51337872\)
463680.kg1	463680kg1	463680.kg	463680kg	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{18} \cdot 3^{9} \cdot 5^{5} \cdot 7^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.700682854$	$1$		$5$	$13271040$	$2.546459$	$292583028222603/8456021875$	$[0, 0, 0, -2389932, 1386122544]$	\(y^2=x^3-2389932x+1386122544\)
463680.le1	463680le1	463680.le	463680le	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{18} \cdot 3^{9} \cdot 5^{5} \cdot 7^{6} \cdot 23 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.365975718$	$1$		$17$	$13271040$	$2.546459$	$292583028222603/8456021875$	$[0, 0, 0, -2389932, -1386122544]$	\(y^2=x^3-2389932x-1386122544\)