Elliptic curve isogeny class with Cremona label 25921b (LMFDB label 25921.a)

• Label: 25921b
• Number of curves: $4$
• Conductor: $25921$
• CM: no
• Rank: $1$

Elliptic curves in class 25921b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25921.a3	25921b1	\([1, -1, 1, -95584, -11061382]\)	\(5545233/161\)	\(2804020163098721\)	\([2]\)	\(126720\)	\(1.7419\)	\(\Gamma_0(N)\)-optimal
25921.a2	25921b2	\([1, -1, 1, -225189, 25487228]\)	\(72511713/25921\)	\(451447246258894081\)	\([2, 2]\)	\(253440\)	\(2.0885\)
25921.a4	25921b3	\([1, -1, 1, 682046, 178628496]\)	\(2014698447/1958887\)	\(-34116513324422138407\)	\([2]\)	\(506880\)	\(2.4351\)
25921.a1	25921b4	\([1, -1, 1, -3206104, 2209901740]\)	\(209267191953/55223\)	\(961778915942861303\)	\([2]\)	\(506880\)	\(2.4351\)

Rank

The elliptic curves in class 25921b have rank \(1\).

Complex multiplication

The elliptic curves in class 25921b do not have complex multiplication.

Modular form 25921.2.a.b

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.