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

• Label: 450840bo
• Number of curves: $2$
• Conductor: $450840$
• CM: no
• Rank: $0$

Elliptic curves in class 450840bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
450840.bo2	450840bo1	\([0, 1, 0, 207984, -38547216]\)	\(40254822716/49359375\)	\(-1220009287536000000\)	\([2]\)	\(4976640\)	\(2.1566\)	\(\Gamma_0(N)\)-optimal^*
450840.bo1	450840bo2	\([0, 1, 0, -1237016, -371475216]\)	\(4234737878642/1247410125\)	\(61664149429219584000\)	\([2]\)	\(9953280\)	\(2.5031\)	\(\Gamma_0(N)\)-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 450840bo1.

Rank

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

Complex multiplication

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

Modular form 450840.2.a.bo

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.