Elliptic curve isogeny class with Cremona label 32448by (LMFDB label 32448.v)

• Label: 32448by
• Number of curves: $2$
• Conductor: $32448$
• CM: no
• Rank: $0$

Elliptic curves in class 32448by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
32448.v2	32448by1	\([0, -1, 0, -1408, 7630]\)	\(1000000/507\)	\(156620298432\)	\([2]\)	\(21504\)	\(0.84059\)	\(\Gamma_0(N)\)-optimal
32448.v1	32448by2	\([0, -1, 0, -12393, -521847]\)	\(10648000/117\)	\(2313161330688\)	\([2]\)	\(43008\)	\(1.1872\)

Rank

The elliptic curves in class 32448by have rank \(0\).

Complex multiplication

The elliptic curves in class 32448by do not have complex multiplication.

Modular form 32448.2.a.by

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.