Elliptic curve isogeny class with Cremona label 450800ed (LMFDB label 450800.ed)

• Label: 450800ed
• Number of curves: $2$
• Conductor: $450800$
• CM: no
• Rank: $0$

Elliptic curves in class 450800ed

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
450800.ed2	450800ed1	\([0, 0, 0, -160475, 115162250]\)	\(-60698457/725788\)	\(-5464846874368000000\)	\([2]\)	\(7077888\)	\(2.2773\)	\(\Gamma_0(N)\)-optimal^*
450800.ed1	450800ed2	\([0, 0, 0, -4668475, 3870326250]\)	\(1494447319737/5411854\)	\(40748749519744000000\)	\([2]\)	\(14155776\)	\(2.6238\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 450800ed1.

Rank

The elliptic curves in class 450800ed have rank \(0\).

Complex multiplication

The elliptic curves in class 450800ed do not have complex multiplication.

Modular form 450800.2.a.ed

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.