Elliptic curve isogeny class with Cremona label 52800fe (LMFDB label 52800.i)

• Label: 52800fe
• Number of curves: $4$
• Conductor: $52800$
• CM: no
• Rank: $1$

Elliptic curves in class 52800fe

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
52800.i3	52800fe1	\([0, -1, 0, -1908, 32562]\)	\(768575296/4455\)	\(4455000000\)	\([2]\)	\(36864\)	\(0.69231\)	\(\Gamma_0(N)\)-optimal
52800.i2	52800fe2	\([0, -1, 0, -3033, -9063]\)	\(48228544/27225\)	\(1742400000000\)	\([2, 2]\)	\(73728\)	\(1.0389\)
52800.i4	52800fe3	\([0, -1, 0, 11967, -84063]\)	\(370146232/219615\)	\(-112442880000000\)	\([2]\)	\(147456\)	\(1.3855\)
52800.i1	52800fe4	\([0, -1, 0, -36033, -2616063]\)	\(10105715528/20625\)	\(10560000000000\)	\([2]\)	\(147456\)	\(1.3855\)

Rank

The elliptic curves in class 52800fe have rank \(1\).

Complex multiplication

The elliptic curves in class 52800fe do not have complex multiplication.

Modular form 52800.2.a.fe

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.