Elliptic curve search results

Results (31 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	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
805.b2	805b2	805.b	805b	$2$	$2$	\( 5 \cdot 7 \cdot 23 \)	\( - 5 \cdot 7^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$0$	$288$	$0.324557$	$-288673724529/311181605$	$1.03586$	$4.10118$	$[1, -1, 1, -138, -1018]$	\(y^2+xy+y=x^3-x^2-138x-1018\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
4025.g2	4025b2	4025.g	4025b	$2$	$2$	\( 5^{2} \cdot 7 \cdot 23 \)	\( - 5^{7} \cdot 7^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$0$	$6912$	$1.129276$	$-288673724529/311181605$	$1.03586$	$4.46936$	$[1, -1, 0, -3442, -130659]$	\(y^2+xy=x^3-x^2-3442x-130659\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
5635.c2	5635j2	5635.c	5635j	$2$	$2$	\( 5 \cdot 7^{2} \cdot 23 \)	\( - 5 \cdot 7^{12} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$0$	$13824$	$1.297512$	$-288673724529/311181605$	$1.03586$	$4.52899$	$[1, -1, 1, -6747, 362576]$	\(y^2+xy+y=x^3-x^2-6747x+362576\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
7245.p2	7245m2	7245.p	7245m	$2$	$2$	\( 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( - 3^{6} \cdot 5 \cdot 7^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.407313448$	$1$		$4$	$9216$	$0.873863$	$-288673724529/311181605$	$1.03586$	$3.82896$	$[1, -1, 0, -1239, 28718]$	\(y^2+xy=x^3-x^2-1239x+28718\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(-26, 220)]$
12880.g2	12880p2	12880.g	12880p	$2$	$2$	\( 2^{4} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{12} \cdot 5 \cdot 7^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$0.907191274$	$1$		$5$	$18432$	$1.017704$	$-288673724529/311181605$	$1.03586$	$3.77856$	$[0, 0, 0, -2203, 67338]$	\(y^2=x^3-2203x+67338\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(-9, 294)]$
18515.g2	18515m2	18515.g	18515m	$2$	$2$	\( 5 \cdot 7 \cdot 23^{2} \)	\( - 5 \cdot 7^{6} \cdot 23^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$0$	$152064$	$1.892303$	$-288673724529/311181605$	$1.03586$	$4.70708$	$[1, -1, 1, -72837, 12819794]$	\(y^2+xy+y=x^3-x^2-72837x+12819794\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
28175.z2	28175c2	28175.z	28175c	$2$	$2$	\( 5^{2} \cdot 7^{2} \cdot 23 \)	\( - 5^{7} \cdot 7^{12} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$0$	$331776$	$2.102230$	$-288673724529/311181605$	$1.03586$	$4.76005$	$[1, -1, 0, -168667, 45153366]$	\(y^2+xy=x^3-x^2-168667x+45153366\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
36225.s2	36225bw2	36225.s	36225bw	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 3^{6} \cdot 5^{7} \cdot 7^{6} \cdot 23^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$0.294131378$	$1$		$34$	$221184$	$1.678583$	$-288673724529/311181605$	$1.03586$	$4.16181$	$[1, -1, 1, -30980, 3558772]$	\(y^2+xy+y=x^3-x^2-30980x+3558772\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(-16, 2020), (-191, 1670)]$
50715.bk2	50715o2	50715.bk	50715o	$2$	$2$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( - 3^{6} \cdot 5 \cdot 7^{12} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$4.163642719$	$1$		$2$	$442368$	$1.846819$	$-288673724529/311181605$	$1.03586$	$4.21890$	$[1, -1, 0, -60720, -9728839]$	\(y^2+xy=x^3-x^2-60720x-9728839\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(1192, 39535)]$
51520.be2	51520y2	51520.be	51520y	$2$	$2$	\( 2^{6} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{18} \cdot 5 \cdot 7^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$10.26516441$	$1$		$1$	$147456$	$1.364279$	$-288673724529/311181605$	$1.03586$	$3.67908$	$[0, 0, 0, -8812, -538704]$	\(y^2=x^3-8812x-538704\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(47160/13, 9508812/13)]$
51520.bp2	51520ce2	51520.bp	51520ce	$2$	$2$	\( 2^{6} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{18} \cdot 5 \cdot 7^{6} \cdot 23^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.528012160$	$1$		$13$	$147456$	$1.364279$	$-288673724529/311181605$	$1.03586$	$3.67908$	$[0, 0, 0, -8812, 538704]$	\(y^2=x^3-8812x+538704\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(10, 672), (45, 483)]$
64400.bb2	64400bi2	64400.bb	64400bi	$2$	$2$	\( 2^{4} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{12} \cdot 5^{7} \cdot 7^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$3.746123364$	$1$		$3$	$442368$	$1.822424$	$-288673724529/311181605$	$1.03586$	$4.10144$	$[0, 0, 0, -55075, 8417250]$	\(y^2=x^3-55075x+8417250\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(335, 5250)]$
90160.bw2	90160co2	90160.bw	90160co	$2$	$2$	\( 2^{4} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( - 2^{12} \cdot 5 \cdot 7^{12} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$4$	$2$	$1$	$884736$	$1.990660$	$-288673724529/311181605$	$1.03586$	$4.15743$	$[0, 0, 0, -107947, -23096934]$	\(y^2=x^3-107947x-23096934\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
92575.u2	92575c2	92575.u	92575c	$2$	$2$	\( 5^{2} \cdot 7 \cdot 23^{2} \)	\( - 5^{7} \cdot 7^{6} \cdot 23^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$0$	$3649536$	$2.697021$	$-288673724529/311181605$	$1.03586$	$4.88904$	$[1, -1, 0, -1820917, 1600653366]$	\(y^2+xy=x^3-x^2-1820917x+1600653366\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
97405.j2	97405e2	97405.j	97405e	$2$	$2$	\( 5 \cdot 7 \cdot 11^{2} \cdot 23 \)	\( - 5 \cdot 7^{6} \cdot 11^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$0$	$403200$	$1.523504$	$-288673724529/311181605$	$1.03586$	$3.64142$	$[1, -1, 0, -16660, 1404585]$	\(y^2+xy=x^3-x^2-16660x+1404585\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
115920.fa2	115920fc2	115920.fa	115920fc	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{12} \cdot 3^{6} \cdot 5 \cdot 7^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$1$	$589824$	$1.567011$	$-288673724529/311181605$	$1.03586$	$3.63185$	$[0, 0, 0, -19827, -1818126]$	\(y^2=x^3-19827x-1818126\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
129605.f2	129605f2	129605.f	129605f	$2$	$2$	\( 5 \cdot 7^{2} \cdot 23^{2} \)	\( - 5 \cdot 7^{12} \cdot 23^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$4.963535417$	$1$		$2$	$7299072$	$2.865261$	$-288673724529/311181605$	$1.03586$	$4.92079$	$[1, -1, 1, -3568998, -4390051438]$	\(y^2+xy+y=x^3-x^2-3568998x-4390051438\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(17341, 2260274)]$
136045.s2	136045s2	136045.s	136045s	$2$	$2$	\( 5 \cdot 7 \cdot 13^{2} \cdot 23 \)	\( - 5 \cdot 7^{6} \cdot 13^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$0$	$622080$	$1.607033$	$-288673724529/311181605$	$1.03586$	$3.62330$	$[1, -1, 0, -23269, -2305770]$	\(y^2+xy=x^3-x^2-23269x-2305770\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
166635.bo2	166635br2	166635.bo	166635br	$2$	$2$	\( 3^{2} \cdot 5 \cdot 7 \cdot 23^{2} \)	\( - 3^{6} \cdot 5 \cdot 7^{6} \cdot 23^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$0$	$4866048$	$2.441612$	$-288673724529/311181605$	$1.03586$	$4.39512$	$[1, -1, 0, -655530, -345478915]$	\(y^2+xy=x^3-x^2-655530x-345478915\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
232645.f2	232645f2	232645.f	232645f	$2$	$2$	\( 5 \cdot 7 \cdot 17^{2} \cdot 23 \)	\( - 5 \cdot 7^{6} \cdot 17^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$3.414379826$	$1$		$2$	$1327104$	$1.741163$	$-288673724529/311181605$	$1.03586$	$3.59623$	$[1, -1, 1, -39792, -5159296]$	\(y^2+xy+y=x^3-x^2-39792x-5159296\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(609, 13702)]$
253575.bf2	253575bf2	253575.bf	253575bf	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( - 3^{6} \cdot 5^{7} \cdot 7^{12} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$0$	$10616832$	$2.651539$	$-288673724529/311181605$	$1.03586$	$4.44927$	$[1, -1, 1, -1518005, -1217622878]$	\(y^2+xy+y=x^3-x^2-1518005x-1217622878\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
257600.cx2	257600cx2	257600.cx	257600cx	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{18} \cdot 5^{7} \cdot 7^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.757552369$	$1$		$3$	$3538944$	$2.168999$	$-288673724529/311181605$	$1.03586$	$3.97889$	$[0, 0, 0, -220300, 67338000]$	\(y^2=x^3-220300x+67338000\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(1490, 55200)]$
257600.dl2	257600dl2	257600.dl	257600dl	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( - 2^{18} \cdot 5^{7} \cdot 7^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$1$	$3538944$	$2.168999$	$-288673724529/311181605$	$1.03586$	$3.97889$	$[0, 0, 0, -220300, -67338000]$	\(y^2=x^3-220300x-67338000\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
290605.k2	290605k2	290605.k	290605k	$2$	$2$	\( 5 \cdot 7 \cdot 19^{2} \cdot 23 \)	\( - 5 \cdot 7^{6} \cdot 19^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$4.026173590$	$1$		$0$	$1741824$	$1.796776$	$-288673724529/311181605$	$1.03586$	$3.58569$	$[1, -1, 0, -49705, 7229166]$	\(y^2+xy=x^3-x^2-49705x+7229166\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(343/2, 14819/2)]$
296240.bw2	296240bw2	296240.bw	296240bw	$2$	$2$	\( 2^{4} \cdot 5 \cdot 7 \cdot 23^{2} \)	\( - 2^{12} \cdot 5 \cdot 7^{6} \cdot 23^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$4$	$2$	$1$	$9732096$	$2.585453$	$-288673724529/311181605$	$1.03586$	$4.33141$	$[0, 0, 0, -1165387, -819301446]$	\(y^2=x^3-1165387x-819301446\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
360640.dr2	360640dr2	360640.dr	360640dr	$2$	$2$	\( 2^{6} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( - 2^{18} \cdot 5 \cdot 7^{12} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$5.961170689$	$1$		$3$	$7077888$	$2.337234$	$-288673724529/311181605$	$1.03586$	$4.03203$	$[0, 0, 0, -431788, 184775472]$	\(y^2=x^3-431788x+184775472\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(344, 8772)]$
360640.eh2	360640eh2	360640.eh	360640eh	$2$	$2$	\( 2^{6} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( - 2^{18} \cdot 5 \cdot 7^{12} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$3.111400819$	$4$	$2$	$5$	$7077888$	$2.337234$	$-288673724529/311181605$	$1.03586$	$4.03203$	$[0, 0, 0, -431788, -184775472]$	\(y^2=x^3-431788x-184775472\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(826, 4704)]$
450800.df2	450800df2	450800.df	450800df	$2$	$2$	\( 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( - 2^{12} \cdot 5^{7} \cdot 7^{12} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$1$	$21233664$	$2.795380$	$-288673724529/311181605$	$1.03586$	$4.38522$	$[0, 0, 0, -2698675, -2887116750]$	\(y^2=x^3-2698675x-2887116750\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
463680.cl2	463680cl2	463680.cl	463680cl	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{18} \cdot 3^{6} \cdot 5 \cdot 7^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$1$	$4718592$	$1.913584$	$-288673724529/311181605$	$1.03586$	$3.56472$	$[0, 0, 0, -79308, 14545008]$	\(y^2=x^3-79308x+14545008\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$
463680.eq2	463680eq2	463680.eq	463680eq	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{18} \cdot 3^{6} \cdot 5 \cdot 7^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$0.942748629$	$1$		$9$	$4718592$	$1.913584$	$-288673724529/311181605$	$1.03586$	$3.56472$	$[0, 0, 0, -79308, -14545008]$	\(y^2=x^3-79308x-14545008\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(642, 14112)]$
487025.m2	487025m2	487025.m	487025m	$2$	$2$	\( 5^{2} \cdot 7 \cdot 11^{2} \cdot 23 \)	\( - 5^{7} \cdot 7^{6} \cdot 11^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1$	$1$		$0$	$9676800$	$2.328224$	$-288673724529/311181605$	$1.03586$	$3.93128$	$[1, -1, 1, -416505, 175156622]$	\(y^2+xy+y=x^3-x^2-416505x+175156622\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[]$