Elliptic curve isogeny class with Cremona label 87360ek (LMFDB label 87360.g)

• Label: 87360ek
• Number of curves: $4$
• Conductor: $87360$
• CM: no
• Rank: $1$

Elliptic curves in class 87360ek

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
87360.g3	87360ek1	\([0, -1, 0, -39436, 3027490]\)	\(105982296177768256/2395575\)	\(153316800\)	\([2]\)	\(147456\)	\(1.0949\)	\(\Gamma_0(N)\)-optimal
87360.g2	87360ek2	\([0, -1, 0, -39481, 3020281]\)	\(1661648641672384/7872125625\)	\(32244226560000\)	\([2, 2]\)	\(294912\)	\(1.4414\)
87360.g4	87360ek3	\([0, -1, 0, -19201, 6098785]\)	\(-23892848985608/475510546875\)	\(-15581529600000000\)	\([2]\)	\(589824\)	\(1.7880\)
87360.g1	87360ek4	\([0, -1, 0, -60481, -520319]\)	\(746685723047048/428258628525\)	\(14033178739507200\)	\([2]\)	\(589824\)	\(1.7880\)

Rank

The elliptic curves in class 87360ek have rank \(1\).

Complex multiplication

The elliptic curves in class 87360ek do not have complex multiplication.

Modular form 87360.2.a.ek

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.