Elliptic curve isogeny class with LMFDB label 54720.ef (Cremona label 54720ev)

• Label: 54720.ef
• Number of curves: $2$
• Conductor: $54720$
• CM: no
• Rank: $1$

Elliptic curves in class 54720.ef

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54720.ef1	54720ev2	\([0, 0, 0, -1601292, -779927024]\)	\(-2376117230685121/342950\)	\(-65538765619200\)	\([]\)	\(414720\)	\(2.0602\)
54720.ef2	54720ev1	\([0, 0, 0, -17292, -1347824]\)	\(-2992209121/2375000\)	\(-453869568000000\)	\([]\)	\(138240\)	\(1.5109\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 54720.ef have rank \(1\).

Complex multiplication

The elliptic curves in class 54720.ef do not have complex multiplication.

Modular form 54720.2.a.ef

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.