Elliptic curves over $\Q$ of conductor 224

Results (4 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
224.a1	224a2	224.a	224a	$2$	$2$	\( 2^{5} \cdot 7 \)	\( 2^{9} \cdot 7^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$56$	$12$	$0$	$0.393548229$	$1$		$7$	$16$	$-0.457201$	$125000/49$	$1.00487$	$3.32143$	$[0, 1, 0, -8, -8]$	\(y^2=x^3+x^2-8x-8\)	2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1	$[(-2, 2)]$
224.a2	224a1	224.a	224a	$2$	$2$	\( 2^{5} \cdot 7 \)	\( - 2^{6} \cdot 7 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$56$	$12$	$0$	$0.787096459$	$1$		$7$	$8$	$-0.803774$	$8000/7$	$0.98030$	$2.42922$	$[0, 1, 0, 2, 0]$	\(y^2=x^3+x^2+2x\)	2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1	$[(1, 2)]$
224.b1	224b2	224.b	224b	$2$	$2$	\( 2^{5} \cdot 7 \)	\( 2^{9} \cdot 7^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$56$	$12$	$0$	$1$	$1$		$1$	$16$	$-0.457201$	$125000/49$	$1.00487$	$3.32143$	$[0, -1, 0, -8, 8]$	\(y^2=x^3-x^2-8x+8\)	2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1	$[]$
224.b2	224b1	224.b	224b	$2$	$2$	\( 2^{5} \cdot 7 \)	\( - 2^{6} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$56$	$12$	$0$	$1$	$1$		$1$	$8$	$-0.803774$	$8000/7$	$0.98030$	$2.42922$	$[0, -1, 0, 2, 0]$	\(y^2=x^3-x^2+2x\)	2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1	$[]$