Elliptic curve isogeny class with LMFDB label 12480.cp (Cremona label 12480dh)

• Label: 12480.cp
• Number of curves: $4$
• Conductor: $12480$
• CM: no
• Rank: $1$

Elliptic curves in class 12480.cp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12480.cp1	12480dh4	\([0, 1, 0, -5025, 135423]\)	\(428320044872/73125\)	\(2396160000\)	\([4]\)	\(12288\)	\(0.80632\)
12480.cp2	12480dh3	\([0, 1, 0, -2145, -37665]\)	\(33324076232/1285245\)	\(42114908160\)	\([2]\)	\(12288\)	\(0.80632\)
12480.cp3	12480dh2	\([0, 1, 0, -345, 1575]\)	\(1111934656/342225\)	\(1401753600\)	\([2, 2]\)	\(6144\)	\(0.45975\)
12480.cp4	12480dh1	\([0, 1, 0, 60, 198]\)	\(367061696/426465\)	\(-27293760\)	\([2]\)	\(3072\)	\(0.11317\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 12480.cp have rank \(1\).

Complex multiplication

The elliptic curves in class 12480.cp do not have complex multiplication.

Modular form 12480.2.a.cp

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.