Elliptic curve isogeny class with Cremona label 10608f (LMFDB label 10608.n)

• Label: 10608f
• Number of curves: $2$
• Conductor: $10608$
• CM: no
• Rank: $2$

Elliptic curves in class 10608f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10608.n1	10608f1	\([0, 1, 0, -424, 3140]\)	\(8251733668/232713\)	\(238298112\)	\([2]\)	\(7168\)	\(0.38624\)	\(\Gamma_0(N)\)-optimal
10608.n2	10608f2	\([0, 1, 0, 96, 10836]\)	\(47279806/24649677\)	\(-50482538496\)	\([2]\)	\(14336\)	\(0.73281\)

Rank

The elliptic curves in class 10608f have rank \(2\).

Complex multiplication

The elliptic curves in class 10608f do not have complex multiplication.

Modular form 10608.2.a.f

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.