Elliptic curve isogeny class with Cremona label 487872er (LMFDB label 487872.er)

• Label: 487872er
• Number of curves: $4$
• Conductor: $487872$
• CM: no
• Rank: $1$

Elliptic curves in class 487872er

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
487872.er4	487872er1	\([0, 0, 0, 242484, 28004240]\)	\(4657463/3696\)	\(-1251282940965421056\)	\([2]\)	\(5898240\)	\(2.1605\)	\(\Gamma_0(N)\)-optimal^*
487872.er3	487872er2	\([0, 0, 0, -1151436, 242667920]\)	\(498677257/213444\)	\(72261589840753065984\)	\([2, 2]\)	\(11796480\)	\(2.5071\)	\(\Gamma_0(N)\)-optimal^*
487872.er1	487872er3	\([0, 0, 0, -15787596, 24134735504]\)	\(1285429208617/614922\)	\(208182199303121928192\)	\([2]\)	\(23592960\)	\(2.8536\)	\(\Gamma_0(N)\)-optimal^*
487872.er2	487872er4	\([0, 0, 0, -8817996, -9910924144]\)	\(223980311017/4278582\)	\(1448516414535095549952\)	\([2]\)	\(23592960\)	\(2.8536\)

^*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 487872er1.

Rank

The elliptic curves in class 487872er have rank \(1\).

Complex multiplication

The elliptic curves in class 487872er do not have complex multiplication.

Modular form 487872.2.a.er

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.