Elliptic curve isogeny class with LMFDB label 162624.fp (Cremona label 162624ex)

• Label: 162624.fp
• Number of curves: $4$
• Conductor: $162624$
• CM: no
• Rank: $1$

Elliptic curves in class 162624.fp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162624.fp1	162624ex4	\([0, 1, 0, -1951649, -1050074049]\)	\(7080974546692/189\)	\(21943093100544\)	\([2]\)	\(2211840\)	\(2.0737\)
162624.fp2	162624ex3	\([0, 1, 0, -189889, 3756575]\)	\(6522128932/3720087\)	\(431905901498007552\)	\([2]\)	\(2211840\)	\(2.0737\)
162624.fp3	162624ex2	\([0, 1, 0, -122129, -16395249]\)	\(6940769488/35721\)	\(1036811149000704\)	\([2, 2]\)	\(1105920\)	\(1.7271\)
162624.fp4	162624ex1	\([0, 1, 0, -3549, -529245]\)	\(-2725888/64827\)	\(-117601264585728\)	\([2]\)	\(552960\)	\(1.3806\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 162624.fp have rank \(1\).

Complex multiplication

The elliptic curves in class 162624.fp do not have complex multiplication.

Modular form 162624.2.a.fp

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.