Elliptic curve isogeny class with Cremona label 388815o (LMFDB label 388815.o)

• Label: 388815o
• Number of curves: $4$
• Conductor: $388815$
• CM: no
• Rank: $1$

Elliptic curves in class 388815o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388815.o4	388815o1	\([1, 1, 1, -5988291, 1480067784]\)	\(1363569097969/734582625\)	\(12793692496658301902625\)	\([2]\)	\(26763264\)	\(2.9330\)	\(\Gamma_0(N)\)-optimal
388815.o2	388815o2	\([1, 1, 1, -74549336, 247422248408]\)	\(2630872462131649/3645140625\)	\(63484769005156980140625\)	\([2, 2]\)	\(53526528\)	\(3.2796\)
388815.o1	388815o3	\([1, 1, 1, -1192392461, 15847593763658]\)	\(10765299591712341649/20708625\)	\(360667093478572988625\)	\([2]\)	\(107053056\)	\(3.6262\)
388815.o3	388815o4	\([1, 1, 1, -53682931, 388921513994]\)	\(-982374577874929/3183837890625\)	\(-55450594045653418212890625\)	\([2]\)	\(107053056\)	\(3.6262\)

Rank

The elliptic curves in class 388815o have rank \(1\).

Complex multiplication

The elliptic curves in class 388815o do not have complex multiplication.

Modular form 388815.2.a.o

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.