Elliptic curve isogeny class with Cremona label 13200a (LMFDB label 13200.p)

• Label: 13200a
• Number of curves: $4$
• Conductor: $13200$
• CM: no
• Rank: $1$

Elliptic curves in class 13200a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13200.p3	13200a1	\([0, -1, 0, -308, 2112]\)	\(810448/33\)	\(132000000\)	\([2]\)	\(4096\)	\(0.32398\)	\(\Gamma_0(N)\)-optimal
13200.p2	13200a2	\([0, -1, 0, -808, -5888]\)	\(3650692/1089\)	\(17424000000\)	\([2, 2]\)	\(8192\)	\(0.67056\)
13200.p1	13200a3	\([0, -1, 0, -11808, -489888]\)	\(5690357426/891\)	\(28512000000\)	\([2]\)	\(16384\)	\(1.0171\)
13200.p4	13200a4	\([0, -1, 0, 2192, -41888]\)	\(36382894/43923\)	\(-1405536000000\)	\([2]\)	\(16384\)	\(1.0171\)

Rank

The elliptic curves in class 13200a have rank \(1\).

Complex multiplication

The elliptic curves in class 13200a do not have complex multiplication.

Modular form 13200.2.a.a

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.