Elliptic curve isogeny class with Cremona label 1344p (LMFDB label 1344.o)

• Label: 1344p
• Number of curves: $4$
• Conductor: $1344$
• CM: no
• Rank: $1$

Elliptic curves in class 1344p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1344.o4	1344p1	\([0, 1, 0, 27, 27]\)	\(2048000/1323\)	\(-1354752\)	\([2]\)	\(192\)	\(-0.13450\)	\(\Gamma_0(N)\)-optimal
1344.o3	1344p2	\([0, 1, 0, -113, 111]\)	\(9826000/5103\)	\(83607552\)	\([2]\)	\(384\)	\(0.21208\)
1344.o2	1344p3	\([0, 1, 0, -453, 3675]\)	\(-10061824000/352947\)	\(-361417728\)	\([2]\)	\(576\)	\(0.41481\)
1344.o1	1344p4	\([0, 1, 0, -7313, 238287]\)	\(2640279346000/3087\)	\(50577408\)	\([2]\)	\(1152\)	\(0.76138\)

Rank

The elliptic curves in class 1344p have rank \(1\).

Complex multiplication

The elliptic curves in class 1344p do not have complex multiplication.

Modular form 1344.2.a.p

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.