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.n3	4830n4	4830.n	4830n	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{6} \cdot 3^{28} \cdot 5^{3} \cdot 7^{2} \cdot 23^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$1$	$1$		$2$	$1290240$	$3.407730$	$-14346048055032350809895395801/2509530875136386550792000$	$[1, 0, 1, -50621638, -158203299112]$	\(y^2+xy+y=x^3-50621638x-158203299112\)
14490.bg3	14490bl4	14490.bg	14490bl	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{6} \cdot 3^{34} \cdot 5^{3} \cdot 7^{2} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6.027216016$	$1$		$2$	$10321920$	$3.957035$	$-14346048055032350809895395801/2509530875136386550792000$	$[1, -1, 1, -455594738, 4271489076017]$	\(y^2+xy+y=x^3-x^2-455594738x+4271489076017\)
24150.by3	24150bt3	24150.by	24150bt	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{6} \cdot 3^{28} \cdot 5^{9} \cdot 7^{2} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$11.91026468$	$1$		$0$	$30965760$	$4.212448$	$-14346048055032350809895395801/2509530875136386550792000$	$[1, 1, 1, -1265540938, -19775412388969]$	\(y^2+xy+y=x^3+x^2-1265540938x-19775412388969\)
33810.l3	33810l3	33810.l	33810l	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( - 2^{6} \cdot 3^{28} \cdot 5^{3} \cdot 7^{8} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6.231999308$	$1$		$2$	$61931520$	$4.380684$	$-14346048055032350809895395801/2509530875136386550792000$	$[1, 1, 0, -2480460238, 54261251135092]$	\(y^2+xy=x^3+x^2-2480460238x+54261251135092\)
38640.bl3	38640ca3	38640.bl	38640ca	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{18} \cdot 3^{28} \cdot 5^{3} \cdot 7^{2} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1$	$4$	$2$	$1$	$30965760$	$4.100876$	$-14346048055032350809895395801/2509530875136386550792000$	$[0, -1, 0, -809946200, 10125011143152]$	\(y^2=x^3-x^2-809946200x+10125011143152\)
72450.bi3	72450bv3	72450.bi	72450bv	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{6} \cdot 3^{34} \cdot 5^{9} \cdot 7^{2} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$0$	$247726080$	$4.761757$	$-14346048055032350809895395801/2509530875136386550792000$	$[1, -1, 0, -11389868442, 533924744633716]$	\(y^2+xy=x^3-x^2-11389868442x+533924744633716\)
101430.eh3	101430fa3	101430.eh	101430fa	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( - 2^{6} \cdot 3^{34} \cdot 5^{3} \cdot 7^{8} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$11.13785709$	$1$		$0$	$495452160$	$4.929993$	$-14346048055032350809895395801/2509530875136386550792000$	$[1, -1, 1, -22324142147, -1465076104789629]$	\(y^2+xy+y=x^3-x^2-22324142147x-1465076104789629\)
111090.z3	111090ba3	111090.z	111090ba	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23^{2} \)	\( - 2^{6} \cdot 3^{28} \cdot 5^{3} \cdot 7^{2} \cdot 23^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$0$	$681246720$	$4.975479$	$-14346048055032350809895395801/2509530875136386550792000$	$[1, 0, 1, -26778846249, 1924805982600172]$	\(y^2+xy+y=x^3-26778846249x+1924805982600172\)
115920.ch3	115920dv3	115920.ch	115920dv	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{18} \cdot 3^{34} \cdot 5^{3} \cdot 7^{2} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$61.43582970$	$1$		$1$	$247726080$	$4.650185$	$-14346048055032350809895395801/2509530875136386550792000$	$[0, 0, 0, -7289515803, -273368011349302]$	\(y^2=x^3-7289515803x-273368011349302\)
154560.c3	154560hs3	154560.c	154560hs	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{24} \cdot 3^{28} \cdot 5^{3} \cdot 7^{2} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1$	$1$		$1$	$247726080$	$4.447449$	$-14346048055032350809895395801/2509530875136386550792000$	$[0, -1, 0, -3239784801, -80996849360415]$	\(y^2=x^3-x^2-3239784801x-80996849360415\)
154560.fz3	154560bo4	154560.fz	154560bo	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{24} \cdot 3^{28} \cdot 5^{3} \cdot 7^{2} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$1$	$1$		$1$	$247726080$	$4.447449$	$-14346048055032350809895395801/2509530875136386550792000$	$[0, 1, 0, -3239784801, 80996849360415]$	\(y^2=x^3+x^2-3239784801x+80996849360415\)
169050.jc3	169050bz4	169050.jc	169050bz	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( - 2^{6} \cdot 3^{28} \cdot 5^{9} \cdot 7^{8} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$0$	$1486356480$	$5.185402$	$-14346048055032350809895395801/2509530875136386550792000$	$[1, 0, 0, -62011505963, 6782780414898417]$	\(y^2+xy=x^3-62011505963x+6782780414898417\)
193200.ds3	193200bx4	193200.ds	193200bx	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{18} \cdot 3^{28} \cdot 5^{9} \cdot 7^{2} \cdot 23^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1$	$1$		$3$	$743178240$	$4.905594$	$-14346048055032350809895395801/2509530875136386550792000$	$[0, 1, 0, -20248655008, 1265585895583988]$	\(y^2=x^3+x^2-20248655008x+1265585895583988\)
270480.fa3	270480fa3	270480.fa	270480fa	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( - 2^{18} \cdot 3^{28} \cdot 5^{3} \cdot 7^{8} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$1486356480$	$5.073830$	$-14346048055032350809895395801/2509530875136386550792000$	$[0, 1, 0, -39687363816, -3472799447373516]$	\(y^2=x^3+x^2-39687363816x-3472799447373516\)
333270.fc3	333270fc3	333270.fc	333270fc	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23^{2} \)	\( - 2^{6} \cdot 3^{34} \cdot 5^{3} \cdot 7^{2} \cdot 23^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1$	$16$	$2$	$0$	$5449973760$	$5.524780$	$-14346048055032350809895395801/2509530875136386550792000$	$[1, -1, 1, -241009616237, -51969761530204651]$	\(y^2+xy+y=x^3-x^2-241009616237x-51969761530204651\)
463680.ke3	463680ke4	463680.ke	463680ke	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{24} \cdot 3^{34} \cdot 5^{3} \cdot 7^{2} \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$20.96796362$	$1$		$1$	$1981808640$	$4.996758$	$-14346048055032350809895395801/2509530875136386550792000$	$[0, 0, 0, -29158063212, 2186944090794416]$	\(y^2=x^3-29158063212x+2186944090794416\)
463680.lc3	463680lc3	463680.lc	463680lc	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{24} \cdot 3^{34} \cdot 5^{3} \cdot 7^{2} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$1981808640$	$4.996758$	$-14346048055032350809895395801/2509530875136386550792000$	$[0, 0, 0, -29158063212, -2186944090794416]$	\(y^2=x^3-29158063212x-2186944090794416\)