Elliptic curve isogeny class with Cremona label 54760c (LMFDB label 54760.e)

• Label: 54760c
• Number of curves: $4$
• Conductor: $54760$
• CM: no
• Rank: $0$

Elliptic curves in class 54760c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54760.e3	54760c1	\([0, 0, 0, -2738, 50653]\)	\(55296/5\)	\(205258112720\)	\([2]\)	\(50688\)	\(0.91010\)	\(\Gamma_0(N)\)-optimal
54760.e2	54760c2	\([0, 0, 0, -9583, -303918]\)	\(148176/25\)	\(16420649017600\)	\([2, 2]\)	\(101376\)	\(1.2567\)
54760.e4	54760c3	\([0, 0, 0, 17797, -1722202]\)	\(237276/625\)	\(-1642064901760000\)	\([2]\)	\(202752\)	\(1.6032\)
54760.e1	54760c4	\([0, 0, 0, -146483, -21578178]\)	\(132304644/5\)	\(13136519214080\)	\([2]\)	\(202752\)	\(1.6032\)

Rank

The elliptic curves in class 54760c have rank \(0\).

Complex multiplication

The elliptic curves in class 54760c do not have complex multiplication.

Modular form 54760.2.a.c

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.