Elliptic curves over $\Q$ of conductor 32674

Results (8 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
32674.a1	32674b2	32674.a	32674b	$2$	$2$	\( 2 \cdot 17 \cdot 31^{2} \)	\( 2^{5} \cdot 17^{2} \cdot 31^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$4216$	$12$	$0$	$1$	$1$		$0$	$307200$	$1.842344$	$450335804625/8887328$	$0.90500$	$4.56375$	$[1, -1, 1, -153460, -22702409]$	\(y^2+xy+y=x^3-x^2-153460x-22702409\)	2.3.0.a.1, 8.6.0.b.1, 2108.6.0.?, 4216.12.0.?	$[]$
32674.a2	32674b1	32674.a	32674b	$2$	$2$	\( 2 \cdot 17 \cdot 31^{2} \)	\( - 2^{10} \cdot 17 \cdot 31^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$4216$	$12$	$0$	$1$	$1$		$1$	$153600$	$1.495770$	$3375/539648$	$1.11262$	$3.96921$	$[1, -1, 1, 300, -1053001]$	\(y^2+xy+y=x^3-x^2+300x-1053001\)	2.3.0.a.1, 8.6.0.c.1, 1054.6.0.?, 4216.12.0.?	$[]$
32674.b1	32674a1	32674.b	32674a	$1$	$1$	\( 2 \cdot 17 \cdot 31^{2} \)	\( - 2^{13} \cdot 17^{3} \cdot 31^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$136$	$2$	$0$	$1$	$1$		$0$	$79560$	$1.374641$	$-1084115556081/40247296$	$0.99913$	$3.99351$	$[1, -1, 1, -20842, -1189463]$	\(y^2+xy+y=x^3-x^2-20842x-1189463\)	136.2.0.?	$[]$
32674.c1	32674c1	32674.c	32674c	$1$	$1$	\( 2 \cdot 17 \cdot 31^{2} \)	\( - 2^{13} \cdot 17^{3} \cdot 31^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$136$	$2$	$0$	$1$	$1$		$0$	$2466360$	$3.091633$	$-1084115556081/40247296$	$0.99913$	$5.97574$	$[1, -1, 1, -20028862, 35595515213]$	\(y^2+xy+y=x^3-x^2-20028862x+35595515213\)	136.2.0.?	$[]$
32674.d1	32674d4	32674.d	32674d	$4$	$6$	\( 2 \cdot 17 \cdot 31^{2} \)	\( 2 \cdot 17^{6} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.4.0.1	2B, 3B	$12648$	$96$	$1$	$1$	$1$		$0$	$362880$	$1.896481$	$159661140625/48275138$	$1.06848$	$4.46399$	$[1, 1, 1, -108613, 9475417]$	\(y^2+xy+y=x^3+x^2-108613x+9475417\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 24.24.0.y.1, $\ldots$	$[]$
32674.d2	32674d3	32674.d	32674d	$4$	$6$	\( 2 \cdot 17 \cdot 31^{2} \)	\( 2^{2} \cdot 17^{3} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.4.0.1	2B, 3B	$12648$	$96$	$1$	$1$	$1$		$1$	$181440$	$1.549908$	$120920208625/19652$	$0.98564$	$4.43726$	$[1, 1, 1, -99003, 11947109]$	\(y^2+xy+y=x^3+x^2-99003x+11947109\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 24.24.0.bw.1, $\ldots$	$[]$
32674.d3	32674d2	32674.d	32674d	$4$	$6$	\( 2 \cdot 17 \cdot 31^{2} \)	\( 2^{3} \cdot 17^{2} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.4.0.1	2B, 3B	$12648$	$96$	$1$	$1$	$1$		$0$	$120960$	$1.347176$	$8805624625/2312$	$0.96590$	$4.18522$	$[1, 1, 1, -41343, -3252067]$	\(y^2+xy+y=x^3+x^2-41343x-3252067\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 24.24.0.y.1, $\ldots$	$[]$
32674.d4	32674d1	32674.d	32674d	$4$	$6$	\( 2 \cdot 17 \cdot 31^{2} \)	\( 2^{6} \cdot 17 \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.4.0.1	2B, 3B	$12648$	$96$	$1$	$1$	$1$		$1$	$60480$	$1.000601$	$3048625/1088$	$0.90010$	$3.41860$	$[1, 1, 1, -2903, -38483]$	\(y^2+xy+y=x^3+x^2-2903x-38483\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 24.24.0.bw.1, $\ldots$	$[]$