Elliptic curve isogeny class with Cremona label 61009b (LMFDB label 61009.b)

• Label: 61009b
• Number of curves: $3$
• Conductor: $61009$
• CM: no
• Rank: $2$

Elliptic curves in class 61009b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
61009.b3	61009b1	\([0, -1, 1, 40673, 125972]\)	\(32768/19\)	\(-4314548154650851\)	\([]\)	\(259200\)	\(1.6895\)	\(\Gamma_0(N)\)-optimal
61009.b2	61009b2	\([0, -1, 1, -569417, 176136937]\)	\(-89915392/6859\)	\(-1557551883828957211\)	\([]\)	\(777600\)	\(2.2388\)
61009.b1	61009b3	\([0, -1, 1, -46936257, 123784336522]\)	\(-50357871050752/19\)	\(-4314548154650851\)	\([]\)	\(2332800\)	\(2.7881\)

Rank

The elliptic curves in class 61009b have rank \(2\).

Complex multiplication

The elliptic curves in class 61009b do not have complex multiplication.

Modular form 61009.2.a.b

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.