Elliptic curve isogeny class with Cremona label 86394l (LMFDB label 86394.i)

• Label: 86394l
• Number of curves: $4$
• Conductor: $86394$
• CM: no
• Rank: $1$

Elliptic curves in class 86394l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
86394.i4	86394l1	\([1, 1, 0, 119, -134075]\)	\(103823/4386816\)	\(-7771512139776\)	\([2]\)	\(276480\)	\(1.1523\)	\(\Gamma_0(N)\)-optimal
86394.i3	86394l2	\([1, 1, 0, -38601, -2883195]\)	\(3590714269297/73410624\)	\(130051398464064\)	\([2, 2]\)	\(552960\)	\(1.4989\)
86394.i2	86394l3	\([1, 1, 0, -82161, 4757229]\)	\(34623662831857/14438442312\)	\(25578581300689032\)	\([2]\)	\(1105920\)	\(1.8455\)
86394.i1	86394l4	\([1, 1, 0, -614561, -185692899]\)	\(14489843500598257/6246072\)	\(11065297558392\)	\([2]\)	\(1105920\)	\(1.8455\)

Rank

The elliptic curves in class 86394l have rank \(1\).

Complex multiplication

The elliptic curves in class 86394l do not have complex multiplication.

Modular form 86394.2.a.l

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.