Elliptic curves over $\Q$ of conductor 289

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
289.a1	289a3	289.a	289a	$4$	$4$	\( 17^{2} \)	\( 17^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.0.20	2B	$1088$	$1536$	$53$	$3.035256177$	$1$		$2$	$288$	$1.039970$	$82483294977/17$	$1.03131$	$7.43593$	$[1, -1, 1, -26209, -1626560]$	\(y^2+xy+y=x^3-x^2-26209x-1626560\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.6, 16.48.0-16.j.1.6, 32.96.0-32.f.2.8, $\ldots$	$[(625, 14715)]$
289.a2	289a2	289.a	289a	$4$	$4$	\( 17^{2} \)	\( 17^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.5	2Cs	$544$	$1536$	$53$	$6.070512355$	$1$		$2$	$144$	$0.693397$	$20346417/289$	$1.02963$	$5.96985$	$[1, -1, 1, -1644, -24922]$	\(y^2+xy+y=x^3-x^2-1644x-24922\)	2.6.0.a.1, 4.24.0-4.a.1.2, 8.48.0-8.f.1.4, 16.96.0-16.c.2.3, 68.48.0-68.b.1.2, $\ldots$	$[(-589/5, 3594/5)]$
289.a3	289a4	289.a	289a	$4$	$4$	\( 17^{2} \)	\( - 17^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.186	2B	$1088$	$1536$	$53$	$3.035256177$	$1$		$0$	$288$	$1.039970$	$-35937/83521$	$1.18071$	$6.31564$	$[1, -1, 1, -199, -68272]$	\(y^2+xy+y=x^3-x^2-199x-68272\)	2.3.0.a.1, 4.12.0.d.1, 8.48.0-8.t.1.4, 16.96.0-16.m.2.3, 68.24.0-4.d.1.1, $\ldots$	$[(239/2, 2647/2)]$
289.a4	289a1	289.a	289a	$4$	$4$	\( 17^{2} \)	\( 17^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.0.12	2B	$1088$	$1536$	$53$	$3.035256177$	$1$		$5$	$72$	$0.346823$	$35937/17$	$1.02432$	$4.85117$	$[1, -1, 1, -199, 510]$	\(y^2+xy+y=x^3-x^2-199x+510\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.8, 16.48.0-16.j.1.8, 32.96.0-32.f.2.7, $\ldots$	$[(-12, 38)]$