Elliptic curve isogeny class with LMFDB label 825.a (Cremona label 825b)

• Label: 825.a
• Number of curves: $4$
• Conductor: $825$
• CM: no
• Rank: $1$

Elliptic curves in class 825.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
825.a1	825b3	\([1, 0, 0, -3663, 84942]\)	\(347873904937/395307\)	\(6176671875\)	\([2]\)	\(768\)	\(0.79209\)
825.a2	825b2	\([1, 0, 0, -288, 567]\)	\(169112377/88209\)	\(1378265625\)	\([2, 2]\)	\(384\)	\(0.44551\)
825.a3	825b1	\([1, 0, 0, -163, -808]\)	\(30664297/297\)	\(4640625\)	\([2]\)	\(192\)	\(0.098940\)	\(\Gamma_0(N)\)-optimal
825.a4	825b4	\([1, 0, 0, 1087, 4692]\)	\(9090072503/5845851\)	\(-91341421875\)	\([2]\)	\(768\)	\(0.79209\)

Rank

The elliptic curves in class 825.a have rank \(1\).

Complex multiplication

The elliptic curves in class 825.a do not have complex multiplication.

Modular form 825.2.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 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.