Elliptic curve isogeny class with Cremona label 453024ca (LMFDB label 453024.ca)

• Label: 453024ca
• Number of curves: $2$
• Conductor: $453024$
• CM: no
• Rank: $1$

Elliptic curves in class 453024ca

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
453024.ca2	453024ca1	\([0, 0, 0, -107085, 5920288]\)	\(1643032000/767637\)	\(63448230228432192\)	\([2]\)	\(3276800\)	\(1.9185\)	\(\Gamma_0(N)\)-optimal^*
453024.ca1	453024ca2	\([0, 0, 0, -1430220, 657961216]\)	\(61162984000/41067\)	\(217238384979652608\)	\([2]\)	\(6553600\)	\(2.2651\)	\(\Gamma_0(N)\)-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 453024ca1.

Rank

The elliptic curves in class 453024ca have rank \(1\).

Complex multiplication

The elliptic curves in class 453024ca do not have complex multiplication.

Modular form 453024.2.a.ca

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.