Elliptic curve isogeny class with LMFDB label 65.a (Cremona label 65a)

• Label: 65.a
• Number of curves: $2$
• Conductor: $65$
• CM: no
• Rank: $1$

Elliptic curves in class 65.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
65.a1	65a1	\([1, 0, 0, -1, 0]\)	\(117649/65\)	\(65\)	\([2]\)	\(2\)	\(-0.96162\)	\(\Gamma_0(N)\)-optimal
65.a2	65a2	\([1, 0, 0, 4, 1]\)	\(6967871/4225\)	\(-4225\)	\([2]\)	\(4\)	\(-0.61504\)

Rank

The elliptic curves in class 65.a have rank \(1\).

Complex multiplication

The elliptic curves in class 65.a do not have complex multiplication.

Modular form 65.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.