Elliptic curve isogeny class with LMFDB label 5577.g (Cremona label 5577g)

• Label: 5577.g
• Number of curves: $6$
• Conductor: $5577$
• CM: no
• Rank: $1$

Elliptic curves in class 5577.g

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
5577.g1	5577g4	[1, 0, 1, -1160020, 480793679]	[2]	43008
5577.g2	5577g5	[1, 0, 1, -508525, -135200167]	[2]	86016
5577.g3	5577g3	[1, 0, 1, -80110, 5834051]	[2, 2]	43008
5577.g4	5577g2	[1, 0, 1, -72505, 7507151]	[2, 2]	21504
5577.g5	5577g1	[1, 0, 1, -4060, 142469]	[2]	10752	\(\Gamma_0(N)\)-optimal
5577.g6	5577g6	[1, 0, 1, 226625, 39820289]	[2]	86016

Rank

The elliptic curves in class 5577.g have rank \(1\).

Modular form 5577.2.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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.