Elliptic curve isogeny class with Cremona label 13552c (LMFDB label 13552.p)

• Label: 13552c
• Number of curves: $4$
• Conductor: $13552$
• CM: no
• Rank: $0$

Elliptic curves in class 13552c

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
13552.p4	13552c1	[0, 0, 0, 121, 2662]	[2]	5120	\(\Gamma_0(N)\)-optimal
13552.p3	13552c2	[0, 0, 0, -2299, 39930]	[2, 2]	10240
13552.p2	13552c3	[0, 0, 0, -7139, -183678]	[2]	20480
13552.p1	13552c4	[0, 0, 0, -36179, 2648690]	[2]	20480

Rank

The elliptic curves in class 13552c have rank \(0\).

Complex multiplication

The elliptic curves in class 13552c do not have complex multiplication.

Modular form 13552.2.a.c

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.