Elliptic curve isogeny class with LMFDB label 414960.dq (Cremona label 414960dq)

• Label: 414960.dq
• Number of curves: $4$
• Conductor: $414960$
• CM: no
• Rank: $1$

Elliptic curves in class 414960.dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
414960.dq1	414960dq4	\([0, -1, 0, -3494520, -2513206800]\)	\(1152196308890224287481/5336644950\)	\(21858897715200\)	\([2]\)	\(6291456\)	\(2.1846\)
414960.dq2	414960dq2	\([0, -1, 0, -218520, -39171600]\)	\(281734042678323481/605361802500\)	\(2479561943040000\)	\([2, 2]\)	\(3145728\)	\(1.8380\)
414960.dq3	414960dq3	\([0, -1, 0, -142520, -66896400]\)	\(-78161746041159481/427424303164950\)	\(-1750729945763635200\)	\([2]\)	\(6291456\)	\(2.1846\)
414960.dq4	414960dq1	\([0, -1, 0, -18520, -131600]\)	\(171518180523481/97256250000\)	\(398361600000000\)	\([2]\)	\(1572864\)	\(1.4915\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 414960.dq1.

Rank

The elliptic curves in class 414960.dq have rank \(1\).

Complex multiplication

The elliptic curves in class 414960.dq do not have complex multiplication.

Modular form 414960.2.a.dq

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.