Elliptic curve isogeny class with Cremona label 490245bu (LMFDB label 490245.bu)

• Label: 490245bu
• Number of curves: $2$
• Conductor: $490245$
• CM: no
• Rank: $0$

Elliptic curves in class 490245bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
490245.bu2	490245bu1	\([1, 0, 1, -330629, 84258731]\)	\(-33974761330806841/6424789539375\)	\(-755870064517929375\)	\([2]\)	\(9510912\)	\(2.1546\)	\(\Gamma_0(N)\)-optimal^*
490245.bu1	490245bu2	\([1, 0, 1, -5510174, 4977892847]\)	\(157264717208387436361/4368589453125\)	\(513960180570703125\)	\([2]\)	\(19021824\)	\(2.5012\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 490245bu1.

Rank

The elliptic curves in class 490245bu have rank \(0\).

Complex multiplication

The elliptic curves in class 490245bu do not have complex multiplication.

Modular form 490245.2.a.bu

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.