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

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

Elliptic curves in class 5040bi

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

Rank

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

Complex multiplication

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

Modular form 5040.2.a.bi

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.