Elliptic curves over $\Q$ of conductor 684

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
684.a1	684b2	684.a	684b	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 19 \)	\( 2^{8} \cdot 3^{12} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$0.754400246$	$1$		$7$	$288$	$0.571862$	$340062928/13851$	$0.89938$	$4.86852$	$[0, 0, 0, -831, -8890]$	\(y^2=x^3-831x-8890\)	2.3.0.a.1, 12.6.0.c.1, 76.6.0.?, 228.12.0.?	$[(-17, 18)]$
684.a2	684b1	684.a	684b	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 19 \)	\( - 2^{4} \cdot 3^{9} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$0.377200123$	$1$		$11$	$144$	$0.225288$	$131072/9747$	$1.13743$	$3.98224$	$[0, 0, 0, 24, -511]$	\(y^2=x^3+24x-511\)	2.3.0.a.1, 6.6.0.a.1, 76.6.0.?, 228.12.0.?	$[(10, 27)]$
684.b1	684a1	684.b	684a	$1$	$1$	\( 2^{2} \cdot 3^{2} \cdot 19 \)	\( - 2^{8} \cdot 3^{6} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$0.140890040$	$1$		$10$	$144$	$0.108375$	$-4194304/19$	$1.07903$	$4.19639$	$[0, 0, 0, -192, 1028]$	\(y^2=x^3-192x+1028\)	38.2.0.a.1	$[(4, 18)]$
684.c1	684c1	684.c	684c	$1$	$1$	\( 2^{2} \cdot 3^{2} \cdot 19 \)	\( - 2^{8} \cdot 3^{8} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$1$	$1$		$0$	$192$	$0.120201$	$8192/171$	$0.94370$	$3.78451$	$[0, 0, 0, 24, -268]$	\(y^2=x^3+24x-268\)	38.2.0.a.1	$[]$