Elliptic curve isogeny class with Cremona label 405720eq (LMFDB label 405720.eq)

• Label: 405720eq
• Number of curves: $2$
• Conductor: $405720$
• CM: no
• Rank: $1$

Elliptic curves in class 405720eq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
405720.eq2	405720eq1	\([0, 0, 0, -14129787, 21318896774]\)	\(-3552342505518244/179863605135\)	\(-15796432610820742487040\)	\([2]\)	\(32440320\)	\(3.0201\)	\(\Gamma_0(N)\)-optimal^*
405720.eq1	405720eq2	\([0, 0, 0, -228755667, 1331695744526]\)	\(7536914291382802562/17961229575\)	\(3154872297550292121600\)	\([2]\)	\(64880640\)	\(3.3667\)	\(\Gamma_0(N)\)-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 405720eq1.

Rank

The elliptic curves in class 405720eq have rank \(1\).

Complex multiplication

The elliptic curves in class 405720eq do not have complex multiplication.

Modular form 405720.2.a.eq

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.