Elliptic curve isogeny class with LMFDB label 471600.de (Cremona label 471600de)

• Label: 471600.de
• Number of curves: $4$
• Conductor: $471600$
• CM: no
• Rank: $0$

Elliptic curves in class 471600.de

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
471600.de1	471600de3	\([0, 0, 0, -20122275, 34742713250]\)	\(19312898130234073/84888\)	\(3960534528000000\)	\([2]\)	\(14155776\)	\(2.6213\)	\(\Gamma_0(N)\)-optimal^*
471600.de2	471600de2	\([0, 0, 0, -1258275, 542281250]\)	\(4722184089433/9884736\)	\(461182242816000000\)	\([2, 2]\)	\(7077888\)	\(2.2747\)	\(\Gamma_0(N)\)-optimal^*
471600.de3	471600de4	\([0, 0, 0, -826275, 920281250]\)	\(-1337180541913/7067998104\)	\(-329764519540224000000\)	\([2]\)	\(14155776\)	\(2.6213\)
471600.de4	471600de1	\([0, 0, 0, -106275, 1993250]\)	\(2845178713/1609728\)	\(75103469568000000\)	\([2]\)	\(3538944\)	\(1.9281\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 471600.de1.

Rank

The elliptic curves in class 471600.de have rank \(0\).

Complex multiplication

The elliptic curves in class 471600.de do not have complex multiplication.

Modular form 471600.2.a.de

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.