Elliptic curve search results

Results (28 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
3822.x2	3822w2	3822.x	3822w	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{18} \cdot 7^{3} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$1$	$1$		$0$	$17280$	$1.510962$	$-16354376146655191/523792501128$	$1.20044$	$5.24031$	$[1, 1, 1, -37017, 2800671]$	\(y^2+xy+y=x^3+x^2-37017x+2800671\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[ ]$
3822.bd2	3822bd2	3822.bd	3822bd	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{18} \cdot 7^{9} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$1$	$1$		$0$	$120960$	$2.483917$	$-16354376146655191/523792501128$	$1.20044$	$6.65577$	$[1, 0, 0, -1813834, -966071716]$	\(y^2+xy=x^3-1813834x-966071716\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[ ]$
11466.h2	11466ba2	11466.h	11466ba	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{24} \cdot 7^{3} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$1$	$1$		$0$	$138240$	$2.060268$	$-16354376146655191/523792501128$	$1.20044$	$5.32960$	$[1, -1, 0, -333153, -75951275]$	\(y^2+xy=x^3-x^2-333153x-75951275\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[ ]$
11466.w2	11466o2	11466.w	11466o	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{24} \cdot 7^{9} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$7.515192658$	$1$		$0$	$967680$	$3.033222$	$-16354376146655191/523792501128$	$1.20044$	$6.57870$	$[1, -1, 0, -16324506, 26083936332]$	\(y^2+xy=x^3-x^2-16324506x+26083936332\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(400299/11, 118893648/11)]$
30576.h2	30576bt2	30576.h	30576bt	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( - 2^{15} \cdot 3^{18} \cdot 7^{9} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$3.267564746$	$1$		$3$	$2903040$	$3.177063$	$-16354376146655191/523792501128$	$1.20044$	$6.12106$	$[0, -1, 0, -29021344, 61828589824]$	\(y^2=x^3-x^2-29021344x+61828589824\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(2336, 82320)]$
30576.cw2	30576db2	30576.cw	30576db	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( - 2^{15} \cdot 3^{18} \cdot 7^{3} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$1.255296204$	$1$		$7$	$414720$	$2.204109$	$-16354376146655191/523792501128$	$1.20044$	$4.99059$	$[0, 1, 0, -592272, -180427500]$	\(y^2=x^3+x^2-592272x-180427500\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(1458, 45360)]$
49686.f2	49686m2	49686.f	49686m	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{3} \cdot 3^{18} \cdot 7^{3} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$1$	$1$		$0$	$2903040$	$2.793434$	$-16354376146655191/523792501128$	$1.20044$	$5.42051$	$[1, 1, 0, -6255876, 6184353960]$	\(y^2+xy=x^3+x^2-6255876x+6184353960\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[ ]$
49686.bm2	49686bi2	49686.bm	49686bi	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{3} \cdot 3^{18} \cdot 7^{9} \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$9.040055587$	$1$		$0$	$20321280$	$3.766392$	$-16354376146655191/523792501128$	$1.20044$	$6.50022$	$[1, 0, 1, -306537950, -2122153022104]$	\(y^2+xy+y=x^3-306537950x-2122153022104\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(2533296/5, 3960931304/5)]$
91728.bw2	91728fu2	91728.bw	91728fu	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{15} \cdot 3^{24} \cdot 7^{3} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$4.755541662$	$1$		$3$	$3317760$	$2.753414$	$-16354376146655191/523792501128$	$1.20044$	$5.08764$	$[0, 0, 0, -5330451, 4866212050]$	\(y^2=x^3-5330451x+4866212050\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(-1582, 96642)]$
91728.fb2	91728eg2	91728.fb	91728eg	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{15} \cdot 3^{24} \cdot 7^{9} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$1$	$25$	$5$	$1$	$23224320$	$3.726368$	$-16354376146655191/523792501128$	$1.20044$	$6.10942$	$[0, 0, 0, -261192099, -1669110733150]$	\(y^2=x^3-261192099x-1669110733150\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[ ]$
95550.cr2	95550bo2	95550.cr	95550bo	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{18} \cdot 5^{6} \cdot 7^{9} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$19.23819277$	$1$		$0$	$15482880$	$3.288635$	$-16354376146655191/523792501128$	$1.20044$	$5.62960$	$[1, 1, 0, -45345850, -120758964500]$	\(y^2+xy=x^3+x^2-45345850x-120758964500\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(3747592635/293, 225958220373010/293)]$
95550.fm2	95550dx2	95550.fm	95550dx	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{18} \cdot 5^{6} \cdot 7^{3} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$0.335141167$	$1$		$10$	$2211840$	$2.315681$	$-16354376146655191/523792501128$	$1.20044$	$4.61146$	$[1, 0, 1, -925426, 351934748]$	\(y^2+xy+y=x^3-925426x+351934748\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(202, 13061)]$
122304.bg2	122304fm2	122304.bg	122304fm	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 3^{18} \cdot 7^{3} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$9.192723168$	$1$		$1$	$3317760$	$2.550682$	$-16354376146655191/523792501128$	$1.20044$	$4.75502$	$[0, -1, 0, -2369089, -1441050911]$	\(y^2=x^3-x^2-2369089x-1441050911\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(241629/11, 56270144/11)]$
122304.dd2	122304ca2	122304.dd	122304ca	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 3^{18} \cdot 7^{9} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$30.96181203$	$1$		$1$	$23224320$	$3.523636$	$-16354376146655191/523792501128$	$1.20044$	$5.75170$	$[0, -1, 0, -116085377, -494512633215]$	\(y^2=x^3-x^2-116085377x-494512633215\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(267640161719569/131719, 2689815301800574878400/131719)]$
122304.fd2	122304dm2	122304.fd	122304dm	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 3^{18} \cdot 7^{3} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$0.457821392$	$1$		$11$	$3317760$	$2.550682$	$-16354376146655191/523792501128$	$1.20044$	$4.75502$	$[0, 1, 0, -2369089, 1441050911]$	\(y^2=x^3+x^2-2369089x+1441050911\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(-325, 46656)]$
122304.ic2	122304ih2	122304.ic	122304ih	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 3^{18} \cdot 7^{9} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$2.132197609$	$1$		$5$	$23224320$	$3.523636$	$-16354376146655191/523792501128$	$1.20044$	$5.75170$	$[0, 1, 0, -116085377, 494512633215]$	\(y^2=x^3+x^2-116085377x+494512633215\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(-6305, 987840)]$
149058.fr2	149058w2	149058.fr	149058w	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{3} \cdot 3^{24} \cdot 7^{9} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$1$	$4$	$2$	$0$	$162570240$	$4.315697$	$-16354376146655191/523792501128$	$1.20044$	$6.45409$	$[1, -1, 1, -2758841546, 57298131596801]$	\(y^2+xy+y=x^3-x^2-2758841546x+57298131596801\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[ ]$
149058.hr2	149058cb2	149058.hr	149058cb	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{3} \cdot 3^{24} \cdot 7^{3} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$1$	$9$	$3$	$0$	$23224320$	$3.342743$	$-16354376146655191/523792501128$	$1.20044$	$5.47395$	$[1, -1, 1, -56302889, -167033859807]$	\(y^2+xy+y=x^3-x^2-56302889x-167033859807\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[ ]$
286650.jo2	286650jo2	286650.jo	286650jo	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{24} \cdot 5^{6} \cdot 7^{3} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$1$	$1$		$0$	$17694720$	$2.864986$	$-16354376146655191/523792501128$	$1.20044$	$4.73286$	$[1, -1, 1, -8328830, -9502238203]$	\(y^2+xy+y=x^3-x^2-8328830x-9502238203\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[ ]$
286650.jy2	286650jy2	286650.jy	286650jy	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{24} \cdot 5^{6} \cdot 7^{9} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$4.507341480$	$1$		$2$	$123863040$	$3.837940$	$-16354376146655191/523792501128$	$1.20044$	$5.66199$	$[1, -1, 1, -408112655, 3260083928847]$	\(y^2+xy+y=x^3-x^2-408112655x+3260083928847\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(39629, 7003110)]$
366912.dd2	366912dd2	366912.dd	366912dd	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 3^{24} \cdot 7^{9} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$64.00990755$	$1$		$1$	$185794560$	$4.072945$	$-16354376146655191/523792501128$	$1.20044$	$5.77299$	$[0, 0, 0, -1044768396, -13352885865200]$	\(y^2=x^3-1044768396x-13352885865200\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(1163352197219396519816081147057/2287830126782, 1240666711810248197586367132891630680901201911/2287830126782)]$
366912.ex2	366912ex2	366912.ex	366912ex	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 3^{24} \cdot 7^{9} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$1$	$1$		$1$	$185794560$	$4.072945$	$-16354376146655191/523792501128$	$1.20044$	$5.77299$	$[0, 0, 0, -1044768396, 13352885865200]$	\(y^2=x^3-1044768396x+13352885865200\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[ ]$
366912.lx2	366912lx2	366912.lx	366912lx	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 3^{24} \cdot 7^{3} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$1$	$1$		$1$	$26542080$	$3.099987$	$-16354376146655191/523792501128$	$1.20044$	$4.86176$	$[0, 0, 0, -21321804, 38929696400]$	\(y^2=x^3-21321804x+38929696400\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[ ]$
366912.nl2	366912nl2	366912.nl	366912nl	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 3^{24} \cdot 7^{3} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$39.15819606$	$1$		$1$	$26542080$	$3.099987$	$-16354376146655191/523792501128$	$1.20044$	$4.86176$	$[0, 0, 0, -21321804, -38929696400]$	\(y^2=x^3-21321804x-38929696400\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(2175017368990836125/16476919, 2468240233841022313660586235/16476919)]$
397488.ei2	397488ei2	397488.ei	397488ei	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{15} \cdot 3^{18} \cdot 7^{9} \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$36.64726433$	$1$		$1$	$487710720$	$4.459541$	$-16354376146655191/523792501128$	$1.20044$	$6.09697$	$[0, -1, 0, -4904607192, 135817793414640]$	\(y^2=x^3-x^2-4904607192x+135817793414640\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(-381892628130714926/2741465, 328264781040039763658316318/2741465)]$
397488.gq2	397488gq2	397488.gq	397488gq	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{15} \cdot 3^{18} \cdot 7^{3} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$1$	$1$		$1$	$69672960$	$3.486584$	$-16354376146655191/523792501128$	$1.20044$	$5.19140$	$[0, 1, 0, -100094024, -395998841484]$	\(y^2=x^3+x^2-100094024x-395998841484\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[ ]$
462462.bw2	462462bw2	462462.bw	462462bw	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 11^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{18} \cdot 7^{3} \cdot 11^{6} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$31.14424168$	$1$		$0$	$22118400$	$2.709908$	$-16354376146655191/523792501128$	$1.20044$	$4.41665$	$[1, 1, 0, -4479059, -3750088635]$	\(y^2+xy=x^3+x^2-4479059x-3750088635\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(298935851633377/238977, 4617719966452352558203/238977)]$
462462.di2	462462di2	462462.di	462462di	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \cdot 11^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{18} \cdot 7^{9} \cdot 11^{6} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2184$	$12$	$0$	$2.451069062$	$1$		$4$	$154828800$	$3.682865$	$-16354376146655191/523792501128$	$1.20044$	$5.31171$	$[1, 0, 1, -219473917, 1285621980080]$	\(y^2+xy+y=x^3-219473917x+1285621980080\)	2.3.0.a.1, 56.6.0.b.1, 312.6.0.?, 1092.6.0.?, 2184.12.0.?	$[(4894, 570911)]$

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