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.ba4	4830ba1	4830.ba	4830ba	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{12} \cdot 3^{8} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.50	2B	$0.317408332$	$1$		$23$	$9216$	$0.964134$	$-164287467238609/757170892800$	$[1, 0, 0, -1141, 44321]$	\(y^2+xy=x^3-1141x+44321\)
14490.t4	14490v1	14490.t	14490v	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{12} \cdot 3^{14} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$1$	$1$		$1$	$73728$	$1.513441$	$-164287467238609/757170892800$	$[1, -1, 0, -10269, -1196667]$	\(y^2+xy=x^3-x^2-10269x-1196667\)
24150.p4	24150m1	24150.p	24150m	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{12} \cdot 3^{8} \cdot 5^{8} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$2.627183669$	$1$		$5$	$221184$	$1.768852$	$-164287467238609/757170892800$	$[1, 1, 0, -28525, 5540125]$	\(y^2+xy=x^3+x^2-28525x+5540125\)
33810.cm4	33810ch1	33810.cm	33810ch	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( - 2^{12} \cdot 3^{8} \cdot 5^{2} \cdot 7^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$1$	$1$		$1$	$442368$	$1.937090$	$-164287467238609/757170892800$	$[1, 1, 1, -55910, -15258013]$	\(y^2+xy+y=x^3+x^2-55910x-15258013\)
38640.v4	38640br1	38640.v	38640br	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{24} \cdot 3^{8} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.60	2B	$5.128356366$	$1$		$15$	$221184$	$1.657282$	$-164287467238609/757170892800$	$[0, -1, 0, -18256, -2836544]$	\(y^2=x^3-x^2-18256x-2836544\)
72450.em4	72450ec1	72450.em	72450ec	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{12} \cdot 3^{14} \cdot 5^{8} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$1$	$1$		$1$	$1769472$	$2.318161$	$-164287467238609/757170892800$	$[1, -1, 1, -256730, -149840103]$	\(y^2+xy+y=x^3-x^2-256730x-149840103\)
101430.v4	101430bg1	101430.v	101430bg	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( - 2^{12} \cdot 3^{14} \cdot 5^{2} \cdot 7^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$1$	$1$		$1$	$3538944$	$2.486397$	$-164287467238609/757170892800$	$[1, -1, 0, -503190, 411463156]$	\(y^2+xy=x^3-x^2-503190x+411463156\)
111090.dn4	111090dm1	111090.dn	111090dm	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23^{2} \)	\( - 2^{12} \cdot 3^{8} \cdot 5^{2} \cdot 7^{2} \cdot 23^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.51	2B	$1$	$1$		$3$	$4866048$	$2.531879$	$-164287467238609/757170892800$	$[1, 0, 0, -603600, -540460800]$	\(y^2+xy=x^3-603600x-540460800\)
115920.es4	115920es1	115920.es	115920es	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{24} \cdot 3^{14} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$2.358598189$	$1$		$5$	$1769472$	$2.206589$	$-164287467238609/757170892800$	$[0, 0, 0, -164307, 76750994]$	\(y^2=x^3-164307x+76750994\)
154560.cq4	154560gy1	154560.cq	154560gy	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{30} \cdot 3^{8} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.103	2B	$1$	$1$		$1$	$1769472$	$2.003857$	$-164287467238609/757170892800$	$[0, -1, 0, -73025, 22765377]$	\(y^2=x^3-x^2-73025x+22765377\)
154560.hu4	154560c1	154560.hu	154560c	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{30} \cdot 3^{8} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.101	2B	$1$	$1$		$1$	$1769472$	$2.003857$	$-164287467238609/757170892800$	$[0, 1, 0, -73025, -22765377]$	\(y^2=x^3+x^2-73025x-22765377\)
169050.de4	169050ge1	169050.de	169050ge	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( - 2^{12} \cdot 3^{8} \cdot 5^{8} \cdot 7^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$1$	$1$		$1$	$10616832$	$2.741810$	$-164287467238609/757170892800$	$[1, 0, 1, -1397751, -1904456102]$	\(y^2+xy+y=x^3-1397751x-1904456102\)
193200.eq4	193200cg1	193200.eq	193200cg	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{24} \cdot 3^{8} \cdot 5^{8} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$3.582453097$	$1$		$5$	$5308416$	$2.462002$	$-164287467238609/757170892800$	$[0, 1, 0, -456408, -355480812]$	\(y^2=x^3+x^2-456408x-355480812\)
270480.ip4	270480ip1	270480.ip	270480ip	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( - 2^{24} \cdot 3^{8} \cdot 5^{2} \cdot 7^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$1$	$1$		$1$	$10616832$	$2.630238$	$-164287467238609/757170892800$	$[0, 1, 0, -894560, 974723700]$	\(y^2=x^3+x^2-894560x+974723700\)
333270.bb4	333270bb1	333270.bb	333270bb	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23^{2} \)	\( - 2^{12} \cdot 3^{14} \cdot 5^{2} \cdot 7^{2} \cdot 23^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$1$	$1$		$1$	$38928384$	$3.081188$	$-164287467238609/757170892800$	$[1, -1, 0, -5432400, 14592441600]$	\(y^2+xy=x^3-x^2-5432400x+14592441600\)
463680.cb4	463680cb1	463680.cb	463680cb	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{30} \cdot 3^{14} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$6.691656036$	$1$		$3$	$14155776$	$2.553162$	$-164287467238609/757170892800$	$[0, 0, 0, -657228, -614007952]$	\(y^2=x^3-657228x-614007952\)
463680.fu4	463680fu1	463680.fu	463680fu	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{30} \cdot 3^{14} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$1$	$1$		$1$	$14155776$	$2.553162$	$-164287467238609/757170892800$	$[0, 0, 0, -657228, 614007952]$	\(y^2=x^3-657228x+614007952\)