Elliptic curve isogeny class with LMFDB label 5040.k (Cremona label 5040bi)

• Label: 5040.k
• Number of curves: $8$
• Conductor: $5040$
• CM: no
• Rank: $0$

Elliptic curves in class 5040.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5040.k1	5040bi7	\([0, 0, 0, -276595203, -1770578063998]\)	\(783736670177727068275201/360150\)	\(1075402137600\)	\([2]\)	\(393216\)	\(3.0369\)
5040.k2	5040bi5	\([0, 0, 0, -17287203, -27665272798]\)	\(191342053882402567201/129708022500\)	\(387306079856640000\)	\([2, 2]\)	\(196608\)	\(2.6903\)
5040.k3	5040bi8	\([0, 0, 0, -17179203, -28028001598]\)	\(-187778242790732059201/4984939585440150\)	\(-14884949843090920857600\)	\([2]\)	\(393216\)	\(3.0369\)
5040.k4	5040bi4	\([0, 0, 0, -2170083, 1230107618]\)	\(378499465220294881/120530818800\)	\(359903096443699200\)	\([2]\)	\(98304\)	\(2.3437\)
5040.k5	5040bi3	\([0, 0, 0, -1087203, -426592798]\)	\(47595748626367201/1215506250000\)	\(3629482214400000000\)	\([2, 2]\)	\(98304\)	\(2.3437\)
5040.k6	5040bi2	\([0, 0, 0, -154083, 13653218]\)	\(135487869158881/51438240000\)	\(153593761628160000\)	\([2, 2]\)	\(49152\)	\(1.9972\)
5040.k7	5040bi1	\([0, 0, 0, 30237, 1524962]\)	\(1023887723039/928972800\)	\(-2773897917235200\)	\([2]\)	\(24576\)	\(1.6506\)	\(\Gamma_0(N)\)-optimal
5040.k8	5040bi6	\([0, 0, 0, 182877, -1363657822]\)	\(226523624554079/269165039062500\)	\(-803722500000000000000\)	\([2]\)	\(196608\)	\(2.6903\)

Rank

The elliptic curves in class 5040.k have rank \(0\).

Complex multiplication

The elliptic curves in class 5040.k do not have complex multiplication.

Modular form 5040.2.a.k

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.