Elliptic curve isogeny class with LMFDB label 13872.w (Cremona label 13872bn)

• Label: 13872.w
• Number of curves: $2$
• Conductor: $13872$
• CM: no
• Rank: $1$

Elliptic curves in class 13872.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13872.w1	13872bn2	\([0, 1, 0, -274357, 55251491]\)	\(-23100424192/14739\)	\(-1457207826395136\)	\([]\)	\(124416\)	\(1.8505\)
13872.w2	13872bn1	\([0, 1, 0, 3083, 318371]\)	\(32768/459\)	\(-45380174524416\)	\([]\)	\(41472\)	\(1.3012\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 13872.w have rank \(1\).

Complex multiplication

The elliptic curves in class 13872.w do not have complex multiplication.

Modular form 13872.2.a.w

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.