Elliptic curve search results

Results (25 matches)

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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	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1326.e1	1326e1	1326.e	1326e	$2$	$2$	\( 2 \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{14} \cdot 3^{8} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$1768$	$12$	$0$	$0.084873081$	$1$		$23$	$1792$	$0.897286$	$612241204436497/308834353152$	$0.98585$	$4.73554$	$[1, 0, 0, -1769, -10407]$	\(y^2+xy=x^3-1769x-10407\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[(-14, 115)]$
3978.d1	3978d1	3978.d	3978d	$2$	$2$	\( 2 \cdot 3^{2} \cdot 13 \cdot 17 \)	\( 2^{14} \cdot 3^{14} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$2.791950280$	$1$		$5$	$14336$	$1.446592$	$612241204436497/308834353152$	$0.98585$	$4.90314$	$[1, -1, 0, -15921, 280989]$	\(y^2+xy=x^3-x^2-15921x+280989\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[(135, 693)]$
10608.d1	10608n1	10608.d	10608n	$2$	$2$	\( 2^{4} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{26} \cdot 3^{8} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$43008$	$1.590433$	$612241204436497/308834353152$	$0.98585$	$4.57053$	$[0, -1, 0, -28304, 666048]$	\(y^2=x^3-x^2-28304x+666048\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
17238.g1	17238d1	17238.g	17238d	$2$	$2$	\( 2 \cdot 3 \cdot 13^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{8} \cdot 13^{8} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$301056$	$2.179760$	$612241204436497/308834353152$	$0.98585$	$5.06802$	$[1, 0, 1, -298965, -22565216]$	\(y^2+xy+y=x^3-298965x-22565216\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
22542.v1	22542u1	22542.v	22542u	$2$	$2$	\( 2 \cdot 3 \cdot 13 \cdot 17^{2} \)	\( 2^{14} \cdot 3^{8} \cdot 13^{2} \cdot 17^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$516096$	$2.313892$	$612241204436497/308834353152$	$0.98585$	$5.09296$	$[1, 1, 1, -511247, -50618347]$	\(y^2+xy+y=x^3+x^2-511247x-50618347\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
31824.bj1	31824bf1	31824.bj	31824bf	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 13 \cdot 17 \)	\( 2^{26} \cdot 3^{14} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$4$	$2$	$1$	$344064$	$2.139740$	$612241204436497/308834353152$	$0.98585$	$4.72200$	$[0, 0, 0, -254739, -17728558]$	\(y^2=x^3-254739x-17728558\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
33150.k1	33150j1	33150.k	33150j	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 2^{14} \cdot 3^{8} \cdot 5^{6} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$2.909032748$	$1$		$3$	$229376$	$1.702005$	$612241204436497/308834353152$	$0.98585$	$4.19883$	$[1, 1, 0, -44225, -1300875]$	\(y^2+xy=x^3+x^2-44225x-1300875\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[(6626, 535823)]$
42432.t1	42432g1	42432.t	42432g	$2$	$2$	\( 2^{6} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{32} \cdot 3^{8} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$344064$	$1.937008$	$612241204436497/308834353152$	$0.98585$	$4.36621$	$[0, -1, 0, -113217, -5215167]$	\(y^2=x^3-x^2-113217x-5215167\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
42432.cn1	42432cj1	42432.cn	42432cj	$2$	$2$	\( 2^{6} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{32} \cdot 3^{8} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$344064$	$1.937008$	$612241204436497/308834353152$	$0.98585$	$4.36621$	$[0, 1, 0, -113217, 5215167]$	\(y^2=x^3+x^2-113217x+5215167\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
51714.t1	51714v1	51714.t	51714v	$2$	$2$	\( 2 \cdot 3^{2} \cdot 13^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{14} \cdot 13^{8} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$2408448$	$2.729069$	$612241204436497/308834353152$	$0.98585$	$5.16235$	$[1, -1, 1, -2690681, 609260825]$	\(y^2+xy+y=x^3-x^2-2690681x+609260825\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
64974.bo1	64974bo1	64974.bo	64974bo	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 2^{14} \cdot 3^{8} \cdot 7^{6} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1.079135633$	$1$		$7$	$516096$	$1.870241$	$612241204436497/308834353152$	$0.98585$	$4.12603$	$[1, 1, 1, -86682, 3482919]$	\(y^2+xy+y=x^3+x^2-86682x+3482919\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[(-11, 2111)]$
67626.d1	67626k1	67626.d	67626k	$2$	$2$	\( 2 \cdot 3^{2} \cdot 13 \cdot 17^{2} \)	\( 2^{14} \cdot 3^{14} \cdot 13^{2} \cdot 17^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$4128768$	$2.863197$	$612241204436497/308834353152$	$0.98585$	$5.18256$	$[1, -1, 0, -4601223, 1362094141]$	\(y^2+xy=x^3-x^2-4601223x+1362094141\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
99450.dt1	99450dc1	99450.dt	99450dc	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 2^{14} \cdot 3^{14} \cdot 5^{6} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$1835008$	$2.251312$	$612241204436497/308834353152$	$0.98585$	$4.37079$	$[1, -1, 1, -398030, 34725597]$	\(y^2+xy+y=x^3-x^2-398030x+34725597\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
127296.n1	127296bv1	127296.n	127296bv	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 13 \cdot 17 \)	\( 2^{32} \cdot 3^{14} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$2752512$	$2.486313$	$612241204436497/308834353152$	$0.98585$	$4.51891$	$[0, 0, 0, -1018956, 141828464]$	\(y^2=x^3-1018956x+141828464\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
127296.bj1	127296dv1	127296.bj	127296dv	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 13 \cdot 17 \)	\( 2^{32} \cdot 3^{14} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$12.65747346$	$1$		$1$	$2752512$	$2.486313$	$612241204436497/308834353152$	$0.98585$	$4.51891$	$[0, 0, 0, -1018956, -141828464]$	\(y^2=x^3-1018956x-141828464\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[(-895360/41, 1089289044/41)]$
137904.bd1	137904br1	137904.bd	137904br	$2$	$2$	\( 2^{4} \cdot 3 \cdot 13^{2} \cdot 17 \)	\( 2^{26} \cdot 3^{8} \cdot 13^{8} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$7225344$	$2.872910$	$612241204436497/308834353152$	$0.98585$	$4.88035$	$[0, -1, 0, -4783432, 1444173808]$	\(y^2=x^3-x^2-4783432x+1444173808\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
160446.o1	160446bf1	160446.o	160446bf	$2$	$2$	\( 2 \cdot 3 \cdot 11^{2} \cdot 13 \cdot 17 \)	\( 2^{14} \cdot 3^{8} \cdot 11^{6} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1.622869149$	$1$		$7$	$2508800$	$2.096233$	$612241204436497/308834353152$	$0.98585$	$4.04110$	$[1, 0, 1, -214052, 13637666]$	\(y^2+xy+y=x^3-214052x+13637666\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[(-63, 5215)]$
180336.cv1	180336t1	180336.cv	180336t	$2$	$2$	\( 2^{4} \cdot 3 \cdot 13 \cdot 17^{2} \)	\( 2^{26} \cdot 3^{8} \cdot 13^{2} \cdot 17^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$2.369620310$	$1$		$5$	$12386304$	$3.007042$	$612241204436497/308834353152$	$0.98585$	$4.90517$	$[0, 1, 0, -8179952, 3223214292]$	\(y^2=x^3+x^2-8179952x+3223214292\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[(4159, 202878)]$
194922.r1	194922cx1	194922.r	194922cx	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 2^{14} \cdot 3^{14} \cdot 7^{6} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$4128768$	$2.419548$	$612241204436497/308834353152$	$0.98585$	$4.29505$	$[1, -1, 0, -780138, -94818956]$	\(y^2+xy=x^3-x^2-780138x-94818956\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
265200.ef1	265200ef1	265200.ef	265200ef	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 2^{26} \cdot 3^{8} \cdot 5^{6} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1.392590744$	$1$		$7$	$5505024$	$2.395153$	$612241204436497/308834353152$	$0.98585$	$4.16572$	$[0, 1, 0, -707608, 81840788]$	\(y^2=x^3+x^2-707608x+81840788\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[(-532, 17550)]$
293046.d1	293046d1	293046.d	293046d	$2$	$2$	\( 2 \cdot 3 \cdot 13^{2} \cdot 17^{2} \)	\( 2^{14} \cdot 3^{8} \cdot 13^{8} \cdot 17^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$3.218601957$	$1$		$3$	$86704128$	$3.596367$	$612241204436497/308834353152$	$0.98585$	$5.27778$	$[1, 1, 0, -86400746, -110776504236]$	\(y^2+xy=x^3+x^2-86400746x-110776504236\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[(-5533, 447659)]$
413712.u1	413712u1	413712.u	413712u	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 13^{2} \cdot 17 \)	\( 2^{26} \cdot 3^{14} \cdot 13^{8} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$57802752$	$3.422215$	$612241204436497/308834353152$	$0.98585$	$4.97546$	$[0, 0, 0, -43050891, -38949641926]$	\(y^2=x^3-43050891x-38949641926\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[ ]$
430950.es1	430950es1	430950.es	430950es	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{8} \cdot 5^{6} \cdot 13^{8} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1.895271308$	$1$		$7$	$38535168$	$2.984482$	$612241204436497/308834353152$	$0.98585$	$4.55493$	$[1, 1, 1, -7474113, -2820651969]$	\(y^2+xy+y=x^3+x^2-7474113x-2820651969\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[(-1985, 65792)]$
478686.b1	478686b1	478686.b	478686b	$2$	$2$	\( 2 \cdot 3 \cdot 13 \cdot 17 \cdot 19^{2} \)	\( 2^{14} \cdot 3^{8} \cdot 13^{2} \cdot 17 \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1.725897696$	$1$		$7$	$12902400$	$2.369507$	$612241204436497/308834353152$	$0.98585$	$3.95409$	$[1, 1, 0, -638616, 70104384]$	\(y^2+xy=x^3+x^2-638616x+70104384\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[(-249, 14745)]$
481338.dj1	481338dj1	481338.dj	481338dj	$2$	$2$	\( 2 \cdot 3^{2} \cdot 11^{2} \cdot 13 \cdot 17 \)	\( 2^{14} \cdot 3^{14} \cdot 11^{6} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$5.506674801$	$1$		$3$	$20070400$	$2.645538$	$612241204436497/308834353152$	$0.98585$	$4.20558$	$[1, -1, 1, -1926464, -368216989]$	\(y^2+xy+y=x^3-x^2-1926464x-368216989\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[(-357, 16729)]$

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