Elliptic curve isogeny class with LMFDB label 25857.e (Cremona label 25857i)

• Label: 25857.e
• Number of curves: $4$
• Conductor: $25857$
• CM: no
• Rank: $2$

Elliptic curves in class 25857.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25857.e1	25857i4	\([1, -1, 1, -137936, 19752490]\)	\(82483294977/17\)	\(59818643937\)	\([2]\)	\(73728\)	\(1.4551\)
25857.e2	25857i2	\([1, -1, 1, -8651, 308026]\)	\(20346417/289\)	\(1016916946929\)	\([2, 2]\)	\(36864\)	\(1.1086\)
25857.e3	25857i1	\([1, -1, 1, -1046, -5300]\)	\(35937/17\)	\(59818643937\)	\([2]\)	\(18432\)	\(0.76200\)	\(\Gamma_0(N)\)-optimal
25857.e4	25857i3	\([1, -1, 1, -1046, 825166]\)	\(-35937/83521\)	\(-293888997662481\)	\([2]\)	\(73728\)	\(1.4551\)

Rank

The elliptic curves in class 25857.e have rank \(2\).

Complex multiplication

The elliptic curves in class 25857.e do not have complex multiplication.

Modular form 25857.2.a.e

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.