Elliptic curve isogeny class with LMFDB label 55545.g (Cremona label 55545u)

• Label: 55545.g
• Number of curves: $4$
• Conductor: $55545$
• CM: no
• Rank: $0$

Elliptic curves in class 55545.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55545.g1	55545u4	\([1, 0, 0, -24334540, -46206373633]\)	\(10765299591712341649/20708625\)	\(3065619711842625\)	\([2]\)	\(2230272\)	\(2.6532\)
55545.g2	55545u2	\([1, 0, 0, -1521415, -721565008]\)	\(2630872462131649/3645140625\)	\(539611632951890625\)	\([2, 2]\)	\(1115136\)	\(2.3067\)
55545.g3	55545u3	\([1, 0, 0, -1095570, -1134038475]\)	\(-982374577874929/3183837890625\)	\(-471322272570556640625\)	\([4]\)	\(2230272\)	\(2.6532\)
55545.g4	55545u1	\([1, 0, 0, -122210, -4332525]\)	\(1363569097969/734582625\)	\(108744591935828625\)	\([2]\)	\(557568\)	\(1.9601\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 55545.g have rank \(0\).

Complex multiplication

The elliptic curves in class 55545.g do not have complex multiplication.

Modular form 55545.2.a.g

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.