Elliptic curve isogeny class with LMFDB label 388080.fd (Cremona label 388080fd)

• Label: 388080.fd
• Number of curves: $4$
• Conductor: $388080$
• CM: no
• Rank: $1$

Elliptic curves in class 388080.fd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388080.fd1	388080fd4	\([0, 0, 0, -110248383, 445560267418]\)	\(6749703004355978704/5671875\)	\(124532407692000000\)	\([2]\)	\(19906560\)	\(3.0158\)
388080.fd2	388080fd3	\([0, 0, 0, -6889008, 6965095543]\)	\(-26348629355659264/24169921875\)	\(-33167367105468750000\)	\([2]\)	\(9953280\)	\(2.6692\)
388080.fd3	388080fd2	\([0, 0, 0, -1391943, 582034642]\)	\(13584145739344/1195803675\)	\(26255217326667436800\)	\([2]\)	\(6635520\)	\(2.4665\)
388080.fd4	388080fd1	\([0, 0, 0, 96432, 42349867]\)	\(72268906496/606436875\)	\(-832187814401790000\)	\([2]\)	\(3317760\)	\(2.1199\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 388080.fd have rank \(1\).

Complex multiplication

The elliptic curves in class 388080.fd do not have complex multiplication.

Modular form 388080.2.a.fd

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.