Elliptic curves over $\Q$ of conductor 361

Results (5 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
361.a1	361a2	361.a	361a	$2$	$19$	\( 19^{2} \)	\( - 19^{9} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-19})$	$-19$	$N(\mathrm{U}(1))$		✓	$19$	19.360.7.18	19B.1.13				$3.444541806$	$1$		$2$	$380$	$1.122070$	$-884736$	$1.31757$	$6.82557$	$[0, 0, 1, -13718, -619025]$	\(y^2+y=x^3-13718x-619025\)		$[(2527, 126891)]$
361.a2	361a1	361.a	361a	$2$	$19$	\( 19^{2} \)	\( - 19^{3} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-19})$	$-19$	$N(\mathrm{U}(1))$		✓	$19$	19.360.7.9	19B.1.6				$0.181291674$	$1$		$4$	$20$	$-0.350149$	$-884736$	$1.31757$	$3.82557$	$[0, 0, 1, -38, 90]$	\(y^2+y=x^3-38x+90\)		$[(0, 9)]$
361.b1	361b3	361.b	361b	$3$	$9$	\( 19^{2} \)	\( - 19^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$1026$	$1296$	$43$	$1$	$1$		$0$	$1080$	$1.505659$	$-50357871050752/19$	$1.10495$	$8.35759$	$[0, -1, 1, -277729, 56427893]$	\(y^2+y=x^3-x^2-277729x+56427893\)	3.4.0.a.1, 6.8.0-3.a.1.2, 9.12.0.a.1, 18.24.0-9.a.1.2, 27.36.0.a.1, $\ldots$	$[]$
361.b2	361b2	361.b	361b	$3$	$9$	\( 19^{2} \)	\( - 19^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.36.0.2	3Cs	$1026$	$1296$	$43$	$1$	$1$		$0$	$360$	$0.956352$	$-89915392/6859$	$1.03310$	$6.13102$	$[0, -1, 1, -3369, 81208]$	\(y^2+y=x^3-x^2-3369x+81208\)	3.12.0.a.1, 6.24.0-3.a.1.1, 9.36.0.b.1, 18.72.0-9.b.1.1, 38.2.0.a.1, $\ldots$	$[]$
361.b3	361b1	361.b	361b	$3$	$9$	\( 19^{2} \)	\( - 19^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$1026$	$1296$	$43$	$1$	$1$		$0$	$120$	$0.407046$	$32768/19$	$1.31757$	$4.76557$	$[0, -1, 1, 241, -17]$	\(y^2+y=x^3-x^2+241x-17\)	3.4.0.a.1, 6.8.0-3.a.1.1, 9.12.0.a.1, 18.24.0-9.a.1.1, 27.36.0.a.1, $\ldots$	$[]$