Elliptic curves over $\Q$ of conductor 89

Results (3 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
89.a1	89a1	89.a	89a	$1$	$1$	\( 89 \)	\( -89 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$356$	$2$	$0$	$0.112104881$	$1$		$6$	$2$	$-0.926876$	$-117649/89$	$0.86393$	$2.78737$	$[1, 1, 1, -1, 0]$	\(y^2+xy+y=x^3+x^2-x\)	356.2.0.?	$[(0, 0)]$
89.b1	89b2	89.b	89b	$2$	$2$	\( 89 \)	\( 89 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.22	2B	$712$	$48$	$0$	$1$	$1$		$1$	$10$	$-0.913497$	$389017/89$	$0.76821$	$2.86755$	$[1, 1, 0, -1, 0]$	\(y^2+xy=x^3+x^2-x\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 178.6.0.?, 356.24.0.?, $\ldots$	$[]$
89.b2	89b1	89.b	89b	$2$	$2$	\( 89 \)	\( - 89^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.37	2B	$712$	$48$	$0$	$1$	$1$		$0$	$5$	$-0.566923$	$4657463/7921$	$0.84673$	$3.56814$	$[1, 1, 0, 4, 5]$	\(y^2+xy=x^3+x^2+4x+5\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 356.12.0.?, 712.48.0.?	$[]$