Elliptic curves over $\Q$ of conductor 6272

Results (16 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
6272.a1	6272h1	6272.a	6272h	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( 2^{7} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	32.48.0.18	2B	$224$	$96$	$0$	$1.435193774$	$1$		$3$	$1152$	$0.116525$	$10976$	$0.88842$	$2.95419$	$[0, 1, 0, -114, -470]$	\(y^2=x^3+x^2-114x-470\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0.h.1, 16.24.0.c.1, 32.48.0.c.1, $\ldots$	$[(23, 98)]$
6272.a2	6272h2	6272.a	6272h	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( - 2^{14} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	32.48.0.21	2B	$224$	$96$	$0$	$2.870387548$	$1$		$3$	$2304$	$0.463099$	$128$	$0.96902$	$3.28886$	$[0, 1, 0, 131, -1989]$	\(y^2=x^3+x^2+131x-1989\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0.g.1, 16.24.0.a.1, 28.12.0-4.a.1.2, $\ldots$	$[(41, 272)]$
6272.b1	6272g2	6272.b	6272g	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( 2^{13} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	32.48.0.18	2B	$224$	$96$	$0$	$1.035144407$	$1$		$5$	$2304$	$0.463099$	$10976$	$0.88842$	$3.42982$	$[0, 1, 0, -457, 3303]$	\(y^2=x^3+x^2-457x+3303\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0.h.1, 16.24.0.c.1, 32.48.0.c.1, $\ldots$	$[(2, 49)]$
6272.b2	6272g1	6272.b	6272g	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( - 2^{8} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	32.48.0.21	2B	$224$	$96$	$0$	$2.070288814$	$1$		$3$	$1152$	$0.116525$	$128$	$0.96902$	$2.81322$	$[0, 1, 0, 33, 265]$	\(y^2=x^3+x^2+33x+265\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0.g.1, 16.24.0.a.1, 28.12.0-4.a.1.1, $\ldots$	$[(3, 20)]$
6272.c1	6272c2	6272.c	6272c	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( 2^{14} \cdot 7^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$56$	$12$	$0$	$1$	$1$		$1$	$3072$	$0.743285$	$432000/7$	$1.03261$	$3.92913$	$[0, 0, 0, -1960, 32928]$	\(y^2=x^3-1960x+32928\)	2.3.0.a.1, 8.6.0.c.1, 28.6.0.a.1, 56.12.0.q.1	$[]$
6272.c2	6272c1	6272.c	6272c	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( 2^{7} \cdot 7^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$56$	$12$	$0$	$1$	$1$		$1$	$1536$	$0.396711$	$108000/49$	$0.90298$	$3.21567$	$[0, 0, 0, -245, -686]$	\(y^2=x^3-245x-686\)	2.3.0.a.1, 8.6.0.b.1, 28.6.0.b.1, 56.12.0.h.1	$[]$
6272.d1	6272e2	6272.d	6272e	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( 2^{13} \cdot 7^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$56$	$12$	$0$	$0.959951091$	$1$		$7$	$3072$	$0.743285$	$108000/49$	$0.90298$	$3.69131$	$[0, 0, 0, -980, 5488]$	\(y^2=x^3-980x+5488\)	2.3.0.a.1, 8.6.0.b.1, 28.6.0.b.1, 56.12.0.h.1	$[(42, 196)]$
6272.d2	6272e1	6272.d	6272e	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( 2^{8} \cdot 7^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$56$	$12$	$0$	$1.919902182$	$1$		$5$	$1536$	$0.396711$	$432000/7$	$1.03261$	$3.45349$	$[0, 0, 0, -490, -4116]$	\(y^2=x^3-490x-4116\)	2.3.0.a.1, 8.6.0.c.1, 28.6.0.a.1, 56.12.0.q.1	$[(-12, 6)]$
6272.e1	6272b2	6272.e	6272b	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( 2^{14} \cdot 7^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$56$	$12$	$0$	$1$	$1$		$1$	$3072$	$0.743285$	$432000/7$	$1.03261$	$3.92913$	$[0, 0, 0, -1960, -32928]$	\(y^2=x^3-1960x-32928\)	2.3.0.a.1, 8.6.0.c.1, 28.6.0.a.1, 56.12.0.q.1	$[]$
6272.e2	6272b1	6272.e	6272b	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( 2^{7} \cdot 7^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$56$	$12$	$0$	$1$	$1$		$1$	$1536$	$0.396711$	$108000/49$	$0.90298$	$3.21567$	$[0, 0, 0, -245, 686]$	\(y^2=x^3-245x+686\)	2.3.0.a.1, 8.6.0.b.1, 28.6.0.b.1, 56.12.0.h.1	$[]$
6272.f1	6272a2	6272.f	6272a	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( 2^{13} \cdot 7^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$56$	$12$	$0$	$1$	$1$		$1$	$3072$	$0.743285$	$108000/49$	$0.90298$	$3.69131$	$[0, 0, 0, -980, -5488]$	\(y^2=x^3-980x-5488\)	2.3.0.a.1, 8.6.0.b.1, 28.6.0.b.1, 56.12.0.h.1	$[]$
6272.f2	6272a1	6272.f	6272a	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( 2^{8} \cdot 7^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$56$	$12$	$0$	$1$	$1$		$1$	$1536$	$0.396711$	$432000/7$	$1.03261$	$3.45349$	$[0, 0, 0, -490, 4116]$	\(y^2=x^3-490x+4116\)	2.3.0.a.1, 8.6.0.c.1, 28.6.0.a.1, 56.12.0.q.1	$[]$
6272.g1	6272f1	6272.g	6272f	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( 2^{7} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	32.48.0.18	2B	$224$	$96$	$0$	$2.310280972$	$1$		$1$	$1152$	$0.116525$	$10976$	$0.88842$	$2.95419$	$[0, -1, 0, -114, 470]$	\(y^2=x^3-x^2-114x+470\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0.h.1, 16.24.0.c.1, 32.48.0.c.1, $\ldots$	$[(73/3, 98/3)]$
6272.g2	6272f2	6272.g	6272f	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( - 2^{14} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	32.48.0.21	2B	$224$	$96$	$0$	$4.620561945$	$1$		$3$	$2304$	$0.463099$	$128$	$0.96902$	$3.28886$	$[0, -1, 0, 131, 1989]$	\(y^2=x^3-x^2+131x+1989\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0.g.1, 16.24.0.a.1, 28.12.0-4.a.1.2, $\ldots$	$[(279, 4656)]$
6272.h1	6272d2	6272.h	6272d	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( 2^{13} \cdot 7^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	32.48.0.18	2B	$224$	$96$	$0$	$1$	$1$		$1$	$2304$	$0.463099$	$10976$	$0.88842$	$3.42982$	$[0, -1, 0, -457, -3303]$	\(y^2=x^3-x^2-457x-3303\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0.h.1, 16.24.0.c.1, 32.48.0.c.1, $\ldots$	$[]$
6272.h2	6272d1	6272.h	6272d	$2$	$2$	\( 2^{7} \cdot 7^{2} \)	\( - 2^{8} \cdot 7^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	32.48.0.21	2B	$224$	$96$	$0$	$1$	$4$	$2$	$1$	$1152$	$0.116525$	$128$	$0.96902$	$2.81322$	$[0, -1, 0, 33, -265]$	\(y^2=x^3-x^2+33x-265\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0.g.1, 16.24.0.a.1, 28.12.0-4.a.1.1, $\ldots$	$[]$