Elliptic curve isogeny class with Cremona label 25200bn (LMFDB label 25200.ed)

• Label: 25200bn
• Number of curves: $4$
• Conductor: $25200$
• CM: no
• Rank: $1$

Elliptic curves in class 25200bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25200.ed4	25200bn1	\([0, 0, 0, -1650, 167375]\)	\(-2725888/64827\)	\(-11814720750000\)	\([2]\)	\(49152\)	\(1.1891\)	\(\Gamma_0(N)\)-optimal
25200.ed3	25200bn2	\([0, 0, 0, -56775, 5183750]\)	\(6940769488/35721\)	\(104162436000000\)	\([2, 2]\)	\(98304\)	\(1.5356\)
25200.ed2	25200bn3	\([0, 0, 0, -88275, -1210750]\)	\(6522128932/3720087\)	\(43391094768000000\)	\([2]\)	\(196608\)	\(1.8822\)
25200.ed1	25200bn4	\([0, 0, 0, -907275, 332626250]\)	\(7080974546692/189\)	\(2204496000000\)	\([2]\)	\(196608\)	\(1.8822\)

Rank

The elliptic curves in class 25200bn have rank \(1\).

Complex multiplication

The elliptic curves in class 25200bn do not have complex multiplication.

Modular form 25200.2.a.bn

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.