Elliptic curve isogeny class with LMFDB label 488189.a (Cremona label 488189a)

• Label: 488189.a
• Number of curves: $2$
• Conductor: $488189$
• CM: no
• Rank: $2$

Elliptic curves in class 488189.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
488189.a1	488189a2	\([1, -1, 1, -25884372, -50681458630]\)	\(177930109857804849/634933\)	\(6844079526487957\)	\([2]\)	\(25436160\)	\(2.6802\)
488189.a2	488189a1	\([1, -1, 1, -1618507, -790840190]\)	\(43499078731809/82055753\)	\(884496630570237737\)	\([2]\)	\(12718080\)	\(2.3337\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 488189.a1.

Rank

The elliptic curves in class 488189.a have rank \(2\).

Complex multiplication

The elliptic curves in class 488189.a do not have complex multiplication.

Modular form 488189.2.a.a

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.