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.s3	4830t2	4830.s	4830t	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.1	2Cs	$0.643012473$	$1$		$14$	$3072$	$0.371714$	$2725812332209/373262400$	$[1, 1, 1, -291, -1791]$	\(y^2+xy+y=x^3+x^2-291x-1791\)
14490.bd3	14490be2	14490.bd	14490be	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{6} \cdot 3^{8} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1.056825676$	$1$		$12$	$24576$	$0.921021$	$2725812332209/373262400$	$[1, -1, 0, -2619, 45733]$	\(y^2+xy=x^3-x^2-2619x+45733\)
24150.x3	24150bd2	24150.x	24150bd	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{8} \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1.972913216$	$1$		$8$	$73728$	$1.176434$	$2725812332209/373262400$	$[1, 0, 1, -7276, -209302]$	\(y^2+xy+y=x^3-7276x-209302\)
33810.db3	33810dg2	33810.db	33810dg	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{8} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1.488636105$	$1$		$8$	$147456$	$1.344669$	$2725812332209/373262400$	$[1, 0, 0, -14260, 571472]$	\(y^2+xy=x^3-14260x+571472\)
38640.cf3	38640cn2	38640.cf	38640cn	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1$	$1$		$3$	$73728$	$1.064861$	$2725812332209/373262400$	$[0, 1, 0, -4656, 105300]$	\(y^2=x^3+x^2-4656x+105300\)
72450.dq3	72450dm2	72450.dq	72450dm	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{6} \cdot 3^{8} \cdot 5^{8} \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1.103597174$	$1$		$14$	$589824$	$1.725739$	$2725812332209/373262400$	$[1, -1, 1, -65480, 5651147]$	\(y^2+xy+y=x^3-x^2-65480x+5651147\)
101430.bg3	101430bo2	101430.bg	101430bo	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{6} \cdot 3^{8} \cdot 5^{2} \cdot 7^{8} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$1179648$	$1.893976$	$2725812332209/373262400$	$[1, -1, 0, -128340, -15429744]$	\(y^2+xy=x^3-x^2-128340x-15429744\)
111090.ch3	111090cf2	111090.ch	111090cf	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23^{2} \)	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 23^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1$	$1$		$2$	$1622016$	$1.939461$	$2725812332209/373262400$	$[1, 1, 1, -153950, 20249435]$	\(y^2+xy+y=x^3+x^2-153950x+20249435\)
115920.cn3	115920ef2	115920.cn	115920ef	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{18} \cdot 3^{8} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$4.435897793$	$1$		$25$	$589824$	$1.614168$	$2725812332209/373262400$	$[0, 0, 0, -41907, -2885006]$	\(y^2=x^3-41907x-2885006\)
154560.ch3	154560cs2	154560.ch	154560cs	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{24} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1$	$1$		$3$	$589824$	$1.411434$	$2725812332209/373262400$	$[0, -1, 0, -18625, 861025]$	\(y^2=x^3-x^2-18625x+861025\)
154560.ih3	154560eh2	154560.ih	154560eh	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{24} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1$	$4$	$2$	$3$	$589824$	$1.411434$	$2725812332209/373262400$	$[0, 1, 0, -18625, -861025]$	\(y^2=x^3+x^2-18625x-861025\)
169050.g3	169050ib2	169050.g	169050ib	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{8} \cdot 7^{8} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1.784007018$	$1$		$12$	$3538944$	$2.149387$	$2725812332209/373262400$	$[1, 1, 0, -356500, 71434000]$	\(y^2+xy=x^3+x^2-356500x+71434000\)
193200.db3	193200ed2	193200.db	193200ed	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{18} \cdot 3^{2} \cdot 5^{8} \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2.548885011$	$1$		$9$	$1769472$	$1.869581$	$2725812332209/373262400$	$[0, -1, 0, -116408, 13395312]$	\(y^2=x^3-x^2-116408x+13395312\)
270480.en3	270480en2	270480.en	270480en	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 7^{8} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3.965144063$	$1$		$7$	$3538944$	$2.037815$	$2725812332209/373262400$	$[0, -1, 0, -228160, -36574208]$	\(y^2=x^3-x^2-228160x-36574208\)
333270.d3	333270d2	333270.d	333270d	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23^{2} \)	\( 2^{6} \cdot 3^{8} \cdot 5^{2} \cdot 7^{2} \cdot 23^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$4.321778705$	$1$		$6$	$12976128$	$2.488766$	$2725812332209/373262400$	$[1, -1, 0, -1385550, -548120300]$	\(y^2+xy=x^3-x^2-1385550x-548120300\)
463680.df3	463680df2	463680.df	463680df	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{24} \cdot 3^{8} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3.493219168$	$1$		$9$	$4718592$	$1.960741$	$2725812332209/373262400$	$[0, 0, 0, -167628, -23080048]$	\(y^2=x^3-167628x-23080048\)
463680.eg3	463680eg2	463680.eg	463680eg	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{24} \cdot 3^{8} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$4718592$	$1.960741$	$2725812332209/373262400$	$[0, 0, 0, -167628, 23080048]$	\(y^2=x^3-167628x+23080048\)