Elliptic curve isogeny class with Cremona label 450840cn (LMFDB label 450840.cn)

• Label: 450840cn
• Number of curves: $4$
• Conductor: $450840$
• CM: no
• Rank: $0$

Elliptic curves in class 450840cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
450840.cn4	450840cn1	\([0, 1, 0, 24180, 1029600]\)	\(253012016/219375\)	\(-1355565875040000\)	\([2]\)	\(1966080\)	\(1.5911\)	\(\Gamma_0(N)\)-optimal^*
450840.cn3	450840cn2	\([0, 1, 0, -120320, 9006000]\)	\(7793764996/3080025\)	\(76128579542246400\)	\([2, 2]\)	\(3932160\)	\(1.9377\)	\(\Gamma_0(N)\)-optimal^*
450840.cn1	450840cn3	\([0, 1, 0, -1680920, 837996720]\)	\(10625310339698/3855735\)	\(190603406557624320\)	\([2]\)	\(7864320\)	\(2.2843\)	\(\Gamma_0(N)\)-optimal^*
450840.cn2	450840cn4	\([0, 1, 0, -871720, -307183120]\)	\(1481943889298/34543665\)	\(1707622599578388480\)	\([2]\)	\(7864320\)	\(2.2843\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 450840cn1.

Rank

The elliptic curves in class 450840cn have rank \(0\).

Complex multiplication

The elliptic curves in class 450840cn do not have complex multiplication.

Modular form 450840.2.a.cn

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.