Elliptic curve isogeny class with LMFDB label 462400.dd (Cremona label 462400dd)

• Label: 462400.dd
• Number of curves: $2$
• Conductor: $462400$
• CM: no
• Rank: $1$

Elliptic curves in class 462400.dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
462400.dd1	462400dd2	\([0, -1, 0, -5442833, 5065843537]\)	\(-115431760/4913\)	\(-758962409580800000000\)	\([]\)	\(9953280\)	\(2.7728\)	\(\Gamma_0(N)\)-optimal^*
462400.dd2	462400dd1	\([0, -1, 0, 337167, 19903537]\)	\(27440/17\)	\(-2626167507200000000\)	\([]\)	\(3317760\)	\(2.2235\)	\(\Gamma_0(N)\)-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 462400.dd1.

Rank

The elliptic curves in class 462400.dd have rank \(1\).

Complex multiplication

The elliptic curves in class 462400.dd do not have complex multiplication.

Modular form 462400.2.a.dd

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.