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

• Label: 488400e
• Number of curves: $4$
• Conductor: $488400$
• CM: no
• Rank: $0$

Elliptic curves in class 488400e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
488400.e4	488400e1	\([0, -1, 0, -9114608, -9131124288]\)	\(1308451928740468777/194033737531392\)	\(12418159202009088000000\)	\([2]\)	\(47185920\)	\(2.9640\)	\(\Gamma_0(N)\)-optimal
488400.e2	488400e2	\([0, -1, 0, -140186608, -638801012288]\)	\(4760617885089919932457/133756441657344\)	\(8560412266070016000000\)	\([2, 2]\)	\(94371840\)	\(3.3106\)
488400.e3	488400e3	\([0, -1, 0, -134554608, -692485236288]\)	\(-4209586785160189454377/801182513521564416\)	\(-51275680865380122624000000\)	\([2]\)	\(188743680\)	\(3.6572\)
488400.e1	488400e4	\([0, -1, 0, -2242970608, -40886086772288]\)	\(19499096390516434897995817/15393430272\)	\(985179537408000000\)	\([2]\)	\(188743680\)	\(3.6572\)

Rank

The elliptic curves in class 488400e have rank \(0\).

Complex multiplication

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

Modular form 488400.2.a.e

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.