Elliptic curve isogeny class with LMFDB label 488400.ej (Cremona label 488400ej)

• Label: 488400.ej
• Number of curves: $4$
• Conductor: $488400$
• CM: no
• Rank: $1$

Elliptic curves in class 488400.ej

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
488400.ej1	488400ej4	\([0, 1, 0, -432239208, 3458726817588]\)	\(139545621883503188502625/220644468\)	\(14121245952000000\)	\([2]\)	\(71663616\)	\(3.2556\)	\(\Gamma_0(N)\)-optimal^*
488400.ej2	488400ej3	\([0, 1, 0, -27015208, 54034769588]\)	\(34069730739753390625/1354703543952\)	\(86701026812928000000\)	\([2]\)	\(35831808\)	\(2.9090\)	\(\Gamma_0(N)\)-optimal^*
488400.ej3	488400ej2	\([0, 1, 0, -5351208, 4715025588]\)	\(264788619837198625/3058196150592\)	\(195724553637888000000\)	\([2]\)	\(23887872\)	\(2.7063\)	\(\Gamma_0(N)\)-optimal^*
488400.ej4	488400ej1	\([0, 1, 0, -615208, -68334412]\)	\(402355893390625/201513996288\)	\(12896895762432000000\)	\([2]\)	\(11943936\)	\(2.3597\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 488400.ej1.

Rank

The elliptic curves in class 488400.ej have rank \(1\).

Complex multiplication

The elliptic curves in class 488400.ej do not have complex multiplication.

Modular form 488400.2.a.ej

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.