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

• Label: 55545g
• Number of curves: $4$
• Conductor: $55545$
• CM: no
• Rank: $1$

Elliptic curves in class 55545g

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
55545.t3	55545g1	[1, 0, 1, -1334, -17869]	[2]	45056	\(\Gamma_0(N)\)-optimal
55545.t2	55545g2	[1, 0, 1, -3979, 74177]	[2, 2]	90112
55545.t4	55545g3	[1, 0, 1, 9246, 465637]	[2]	180224
55545.t1	55545g4	[1, 0, 1, -59524, 5584241]	[2]	180224

Rank

The elliptic curves in class 55545g have rank \(1\).

Complex multiplication

The elliptic curves in class 55545g 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 Cremona 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 Cremona labels.