Elliptic curve isogeny class with Cremona label 22848bu (LMFDB label 22848.e)

• Label: 22848bu
• Number of curves: $4$
• Conductor: $22848$
• CM: no
• Rank: $2$

Elliptic curves in class 22848bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
22848.e4	22848bu1	\([0, -1, 0, 111, 369]\)	\(9148592/9639\)	\(-157925376\)	\([2]\)	\(6144\)	\(0.25985\)	\(\Gamma_0(N)\)-optimal
22848.e3	22848bu2	\([0, -1, 0, -609, 3969]\)	\(381775972/127449\)	\(8352497664\)	\([2, 2]\)	\(12288\)	\(0.60642\)
22848.e2	22848bu3	\([0, -1, 0, -3969, -92127]\)	\(52767497666/1753941\)	\(229892554752\)	\([2]\)	\(24576\)	\(0.95300\)
22848.e1	22848bu4	\([0, -1, 0, -8769, 318945]\)	\(569001644066/122451\)	\(16049897472\)	\([2]\)	\(24576\)	\(0.95300\)

Rank

The elliptic curves in class 22848bu have rank \(2\).

Complex multiplication

The elliptic curves in class 22848bu do not have complex multiplication.

Modular form 22848.2.a.bu

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.