Elliptic curves over $\Q$ of conductor 578

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
578.a1	578a4	578.a	578a	$4$	$6$	\( 2 \cdot 17^{2} \)	\( 2 \cdot 17^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.4.0.1	2B, 3B	$408$	$96$	$1$	$1$	$9$	$3$	$0$	$3456$	$1.596094$	$159661140625/48275138$	$1.06848$	$6.72932$	$[1, 1, 1, -32663, -1583717]$	\(y^2+xy+y=x^3+x^2-32663x-1583717\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 12.24.0-6.a.1.5, $\ldots$	$[]$
578.a2	578a3	578.a	578a	$4$	$6$	\( 2 \cdot 17^{2} \)	\( 2^{2} \cdot 17^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.4.0.1	2B, 3B	$408$	$96$	$1$	$1$	$9$	$3$	$1$	$1728$	$1.249521$	$120920208625/19652$	$0.98564$	$6.68562$	$[1, 1, 1, -29773, -1989473]$	\(y^2+xy+y=x^3+x^2-29773x-1989473\)	2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.3, 8.6.0.c.1, 24.48.0-24.bw.1.6, $\ldots$	$[]$
578.a3	578a2	578.a	578a	$4$	$6$	\( 2 \cdot 17^{2} \)	\( 2^{3} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.4.0.1	2B, 3B	$408$	$96$	$1$	$1$	$1$		$0$	$1152$	$1.046787$	$8805624625/2312$	$0.96590$	$6.27368$	$[1, 1, 1, -12433, 528295]$	\(y^2+xy+y=x^3+x^2-12433x+528295\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 12.24.0-6.a.1.11, $\ldots$	$[]$
578.a4	578a1	578.a	578a	$4$	$6$	\( 2 \cdot 17^{2} \)	\( 2^{6} \cdot 17^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.4.0.1	2B, 3B	$408$	$96$	$1$	$1$	$1$		$1$	$576$	$0.700214$	$3048625/1088$	$0.90010$	$5.02070$	$[1, 1, 1, -873, 5783]$	\(y^2+xy+y=x^3+x^2-873x+5783\)	2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.1, 8.6.0.c.1, 24.48.0-24.bw.1.2, $\ldots$	$[]$