Elliptic curve isogeny class with Cremona label 55488bj (LMFDB label 55488.ed)

• Label: 55488bj
• Number of curves: $4$
• Conductor: $55488$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 55488bj have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 55488bj do not have complex multiplication.

Modular form 55488.2.a.bj

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.

Elliptic curves in class 55488bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55488.ed3	55488bj1	\([0, 1, 0, -1252, -17158]\)	\(140608/3\)	\(4634413248\)	\([2]\)	\(36864\)	\(0.64381\)	\(\Gamma_0(N)\)-optimal
55488.ed2	55488bj2	\([0, 1, 0, -2697, 28215]\)	\(21952/9\)	\(889807343616\)	\([2, 2]\)	\(73728\)	\(0.99039\)
55488.ed4	55488bj3	\([0, 1, 0, 8863, 215487]\)	\(97336/81\)	\(-64066128740352\)	\([2]\)	\(147456\)	\(1.3370\)
55488.ed1	55488bj4	\([0, 1, 0, -37377, 2767935]\)	\(7301384/3\)	\(2372819582976\)	\([2]\)	\(147456\)	\(1.3370\)