Elliptic curve isogeny class with LMFDB label 2005.a (Cremona label 2005b)

• Label: 2005.a
• Number of curves: $2$
• Conductor: $2005$
• CM: no
• Rank: $1$

Elliptic curves in class 2005.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2005.a1	2005b1	\([1, -1, 1, -7, 6]\)	\(33076161/10025\)	\(10025\)	\([2]\)	\(96\)	\(-0.52721\)	\(\Gamma_0(N)\)-optimal
2005.a2	2005b2	\([1, -1, 1, 18, 26]\)	\(679151439/804005\)	\(-804005\)	\([2]\)	\(192\)	\(-0.18063\)

Rank

The elliptic curves in class 2005.a have rank \(1\).

Complex multiplication

The elliptic curves in class 2005.a do not have complex multiplication.

Modular form 2005.2.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.