Elliptic curve isogeny class with LMFDB label 400554.de (Cremona label 400554de)

• Label: 400554.de
• Number of curves: $4$
• Conductor: $400554$
• CM: no
• Rank: $0$

Elliptic curves in class 400554.de

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
400554.de1	400554de3	\([1, -1, 1, -589181, 174144107]\)	\(1285429208617/614922\)	\(10820344487166522\)	\([2]\)	\(4718592\)	\(2.0316\)	\(\Gamma_0(N)\)-optimal^*
400554.de2	400554de4	\([1, -1, 1, -329081, -71369485]\)	\(223980311017/4278582\)	\(75287160252178182\)	\([2]\)	\(4718592\)	\(2.0316\)
400554.de3	400554de2	\([1, -1, 1, -42971, 1760231]\)	\(498677257/213444\)	\(3755822053396644\)	\([2, 2]\)	\(2359296\)	\(1.6850\)	\(\Gamma_0(N)\)-optimal^*
400554.de4	400554de1	\([1, -1, 1, 9049, 199631]\)	\(4657463/3696\)	\(-65035879712496\)	\([2]\)	\(1179648\)	\(1.3384\)	\(\Gamma_0(N)\)-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 400554.de1.

Rank

The elliptic curves in class 400554.de have rank \(0\).

Complex multiplication

The elliptic curves in class 400554.de do not have complex multiplication.

Modular form 400554.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.