Elliptic curve isogeny class with Cremona label 431970dz (LMFDB label 431970.dz)

• Label: 431970dz
• Number of curves: $2$
• Conductor: $431970$
• CM: no
• Rank: $1$

Elliptic curves in class 431970dz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
431970.dz2	431970dz1	\([1, 1, 1, 9859, -445741]\)	\(59822347031/83966400\)	\(-148751599550400\)	\([2]\)	\(1612800\)	\(1.4051\)	\(\Gamma_0(N)\)-optimal^*
431970.dz1	431970dz2	\([1, 1, 1, -62741, -4482301]\)	\(15417797707369/4080067320\)	\(7228088141486520\)	\([2]\)	\(3225600\)	\(1.7516\)	\(\Gamma_0(N)\)-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 431970dz1.

Rank

The elliptic curves in class 431970dz have rank \(1\).

Complex multiplication

The elliptic curves in class 431970dz do not have complex multiplication.

Modular form 431970.2.a.dz

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.