Elliptic curves over $\Q$ of conductor 4641

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	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation	mod-$m$ images
4641.a1	4641f1	4641.a	4641f	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( - 3^{2} \cdot 7 \cdot 13^{3} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$182$	$2$	$0$	$0.748684411$	$1$		$4$	$2208$	$0.138159$	$-325660672/40000779$	$[0, 1, 1, -14, -310]$	\(y^2+y=x^3+x^2-14x-310\)	182.2.0.?
4641.b1	4641b5	4641.b	4641b	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 7^{2} \cdot 13^{8} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.55	2B	$74256$	$192$	$1$	$0.521669926$	$1$		$8$	$12288$	$1.381887$	$7389727131216686257/6115533215337$	$[1, 1, 1, -40579, -3160960]$	\(y^2+xy+y=x^3+x^2-40579x-3160960\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 34.6.0.a.1, 68.24.0-68.g.1.1, $\ldots$
4641.b2	4641b3	4641.b	4641b	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 7^{4} \cdot 13^{4} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.6	2Cs	$37128$	$192$	$1$	$1.043339852$	$1$		$8$	$6144$	$1.035313$	$3275619238041697/1605271262049$	$[1, 1, 1, -3094, -27214]$	\(y^2+xy+y=x^3+x^2-3094x-27214\)	2.6.0.a.1, 4.24.0-4.b.1.1, 68.48.0-68.c.1.2, 104.48.0.?, 168.48.0.?, $\ldots$
4641.b3	4641b2	4641.b	4641b	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 7^{2} \cdot 13^{2} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.5	2Cs	$37128$	$192$	$1$	$2.086679704$	$1$		$14$	$3072$	$0.688740$	$495909170514577/6224736609$	$[1, 1, 1, -1649, 24806]$	\(y^2+xy+y=x^3+x^2-1649x+24806\)	2.6.0.a.1, 4.24.0-4.b.1.3, 104.48.0.?, 136.48.0.?, 168.48.0.?, $\ldots$
4641.b4	4641b1	4641.b	4641b	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.45	2B	$74256$	$192$	$1$	$4.173359409$	$1$		$5$	$1536$	$0.342166$	$491411892194497/78897$	$[1, 1, 1, -1644, 24972]$	\(y^2+xy+y=x^3+x^2-1644x+24972\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 208.48.0.?, 272.48.0.?, $\ldots$
4641.b5	4641b4	4641.b	4641b	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( - 3 \cdot 7 \cdot 13 \cdot 17^{8} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.45	2B	$74256$	$192$	$1$	$4.173359409$	$1$		$4$	$6144$	$1.035313$	$-2533811507137/1904381781393$	$[1, 1, 1, -284, 66302]$	\(y^2+xy+y=x^3+x^2-284x+66302\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 104.48.0.?, 168.48.0.?, $\ldots$
4641.b6	4641b6	4641.b	4641b	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( - 3^{8} \cdot 7^{8} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.55	2B	$74256$	$192$	$1$	$2.086679704$	$1$		$2$	$12288$	$1.381887$	$158346567380527343/108665074944153$	$[1, 1, 1, 11271, -193848]$	\(y^2+xy+y=x^3+x^2+11271x-193848\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 68.24.0-68.h.1.1, 104.48.0.?, $\ldots$
4641.c1	4641a3	4641.c	4641a	$4$	$4$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$37128$	$48$	$0$	$6.227030391$	$4$	$2$	$2$	$5120$	$0.821942$	$1677087406638588673/4641$	$[1, 1, 1, -24752, -1509184]$	\(y^2+xy+y=x^3+x^2-24752x-1509184\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 68.12.0-4.c.1.1, 136.24.0.?, $\ldots$
4641.c2	4641a2	4641.c	4641a	$4$	$4$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 7^{2} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$18564$	$48$	$0$	$3.113515195$	$1$		$6$	$2560$	$0.475369$	$409460675852593/21538881$	$[1, 1, 1, -1547, -24064]$	\(y^2+xy+y=x^3+x^2-1547x-24064\)	2.6.0.a.1, 4.12.0-2.a.1.1, 68.24.0-68.a.1.2, 1092.24.0.?, 18564.48.0.?
4641.c3	4641a4	4641.c	4641a	$4$	$4$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( - 3^{4} \cdot 7^{4} \cdot 13^{4} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$37128$	$48$	$0$	$1.556757597$	$1$		$4$	$5120$	$0.821942$	$-345608484635233/94427721297$	$[1, 1, 1, -1462, -26716]$	\(y^2+xy+y=x^3+x^2-1462x-26716\)	2.3.0.a.1, 4.12.0-4.c.1.2, 68.24.0-68.h.1.1, 2184.24.0.?, 37128.48.0.?
4641.c4	4641a1	4641.c	4641a	$4$	$4$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 3 \cdot 7 \cdot 13 \cdot 17^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$37128$	$48$	$0$	$6.227030391$	$1$		$3$	$1280$	$0.128795$	$117433042273/22801233$	$[1, 1, 1, -102, -366]$	\(y^2+xy+y=x^3+x^2-102x-366\)	2.3.0.a.1, 4.12.0-4.c.1.1, 136.24.0.?, 546.6.0.?, 1092.24.0.?, $\ldots$
4641.d1	4641g1	4641.d	4641g	$2$	$2$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 3^{5} \cdot 7 \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$18564$	$12$	$0$	$0.353473160$	$1$		$9$	$2240$	$0.248647$	$10418796526321/6390657$	$[1, 0, 0, -455, 3696]$	\(y^2+xy=x^3-455x+3696\)	2.3.0.a.1, 68.6.0.b.1, 546.6.0.?, 18564.12.0.?
4641.d2	4641g2	4641.d	4641g	$2$	$2$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( - 3^{10} \cdot 7^{2} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$18564$	$12$	$0$	$0.176736580$	$1$		$12$	$4480$	$0.595221$	$-5602762882081/8312741073$	$[1, 0, 0, -370, 5141]$	\(y^2+xy=x^3-370x+5141\)	2.3.0.a.1, 68.6.0.a.1, 1092.6.0.?, 18564.12.0.?
4641.e1	4641d1	4641.e	4641d	$2$	$2$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 3^{3} \cdot 7 \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$18564$	$12$	$0$	$1.249520914$	$1$		$3$	$768$	$-0.128720$	$10431681625/710073$	$[1, 0, 1, -46, 107]$	\(y^2+xy+y=x^3-46x+107\)	2.3.0.a.1, 68.6.0.b.1, 546.6.0.?, 18564.12.0.?
4641.e2	4641d2	4641.e	4641d	$2$	$2$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( - 3^{6} \cdot 7^{2} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$18564$	$12$	$0$	$0.624760457$	$1$		$4$	$1536$	$0.217854$	$6804992375/102626433$	$[1, 0, 1, 39, 481]$	\(y^2+xy+y=x^3+39x+481\)	2.3.0.a.1, 68.6.0.a.1, 1092.6.0.?, 18564.12.0.?
4641.f1	4641c1	4641.f	4641c	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( - 3^{22} \cdot 7 \cdot 13 \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$182$	$2$	$0$	$3.413422435$	$1$		$0$	$32736$	$1.563702$	$-1302227927110660096/825290486657091$	$[0, -1, 1, -22750, 1919349]$	\(y^2+y=x^3-x^2-22750x+1919349\)	182.2.0.?
4641.g1	4641e1	4641.g	4641e	$1$	$1$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( - 3^{6} \cdot 7 \cdot 13 \cdot 17^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$182$	$2$	$0$	$1$	$1$		$0$	$4128$	$0.576782$	$-2731787761881088/19171971$	$[0, 1, 1, -2912, -61465]$	\(y^2+y=x^3+x^2-2912x-61465\)	182.2.0.?