Elliptic curve isogeny class with Cremona label 2448o (LMFDB label 2448.o)

• Label: 2448o
• Number of curves: $4$
• Conductor: $2448$
• CM: no
• Rank: $1$

Elliptic curves in class 2448o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2448.o4	2448o1	\([0, 0, 0, -99, 162]\)	\(35937/17\)	\(50761728\)	\([2]\)	\(512\)	\(0.17267\)	\(\Gamma_0(N)\)-optimal
2448.o2	2448o2	\([0, 0, 0, -819, -8910]\)	\(20346417/289\)	\(862949376\)	\([2, 2]\)	\(1024\)	\(0.51924\)
2448.o1	2448o3	\([0, 0, 0, -13059, -574398]\)	\(82483294977/17\)	\(50761728\)	\([2]\)	\(2048\)	\(0.86582\)
2448.o3	2448o4	\([0, 0, 0, -99, -24030]\)	\(-35937/83521\)	\(-249392369664\)	\([2]\)	\(2048\)	\(0.86582\)

Rank

The elliptic curves in class 2448o have rank \(1\).

Complex multiplication

The elliptic curves in class 2448o do not have complex multiplication.

Modular form 2448.2.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.