Elliptic curves over $\Q$ of conductor 242

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
242.a1	242b2	242.a	242b	$2$	$3$	\( 2 \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.4.0.2, 3.8.0.2	3B.1.2	$24$	$32$	$0$	$1$	$1$		$0$	$528$	$1.067739$	$-128667913/4096$	$0.98675$	$6.90652$	$[1, 0, 1, -6295, -197958]$	\(y^2+xy+y=x^3-6295x-197958\)	3.8.0-3.a.1.1, 4.2.0.a.1, 8.4.0-4.a.1.1, 12.16.0-12.a.1.5, 24.32.0-24.b.2.8	$[]$
242.a2	242b1	242.a	242b	$2$	$3$	\( 2 \cdot 11^{2} \)	\( - 2^{4} \cdot 11^{8} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.4.0.2, 3.8.0.1	3B.1.1	$24$	$32$	$0$	$1$	$1$		$2$	$176$	$0.518434$	$24167/16$	$0.94416$	$5.33362$	$[1, 0, 1, 360, -970]$	\(y^2+xy+y=x^3+360x-970\)	3.8.0-3.a.1.2, 4.2.0.a.1, 8.4.0-4.a.1.1, 12.16.0-12.a.1.6, 24.32.0-24.b.1.8	$[]$
242.b1	242a2	242.b	242a	$2$	$3$	\( 2 \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.2.0.1, 3.4.0.1	3B	$264$	$32$	$0$	$0.041190460$	$1$		$14$	$48$	$-0.131208$	$-128667913/4096$	$0.98675$	$4.28536$	$[1, 0, 0, -52, 144]$	\(y^2+xy=x^3-52x+144\)	3.4.0.a.1, 4.2.0.a.1, 12.8.0.a.1, 24.16.0.b.2, 33.8.0-3.a.1.1, $\ldots$	$[(8, 12)]$
242.b2	242a1	242.b	242a	$2$	$3$	\( 2 \cdot 11^{2} \)	\( - 2^{4} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.2.0.1, 3.4.0.1	3B	$264$	$32$	$0$	$0.123571382$	$1$		$8$	$16$	$-0.680514$	$24167/16$	$0.94416$	$2.71246$	$[1, 0, 0, 3, 1]$	\(y^2+xy=x^3+3x+1\)	3.4.0.a.1, 4.2.0.a.1, 12.8.0.a.1, 24.16.0.b.1, 33.8.0-3.a.1.2, $\ldots$	$[(0, 1)]$