Elliptic curve isogeny class with LMFDB label 20691.i (Cremona label 20691o)

• Label: 20691.i
• Number of curves: $3$
• Conductor: $20691$
• CM: no
• Rank: $1$

Elliptic curves in class 20691.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20691.i1	20691o3	\([0, 0, 1, -837804, -295162893]\)	\(-50357871050752/19\)	\(-24537891411\)	\([]\)	\(97200\)	\(1.7817\)
20691.i2	20691o2	\([0, 0, 1, -10164, -419598]\)	\(-89915392/6859\)	\(-8858178799371\)	\([]\)	\(32400\)	\(1.2324\)
20691.i3	20691o1	\([0, 0, 1, 726, -333]\)	\(32768/19\)	\(-24537891411\)	\([]\)	\(10800\)	\(0.68308\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 20691.i have rank \(1\).

Complex multiplication

The elliptic curves in class 20691.i do not have complex multiplication.

Modular form 20691.2.a.i

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.