Elliptic curve isogeny class with Cremona label 55488j (LMFDB label 55488.bs)

• Label: 55488j
• Number of curves: $4$
• Conductor: $55488$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 55488j have rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 55488.2.a.j

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 55488j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55488.bs3	55488j1	\([0, -1, 0, -1252, 17158]\)	\(140608/3\)	\(4634413248\)	\([2]\)	\(36864\)	\(0.64381\)	\(\Gamma_0(N)\)-optimal
55488.bs2	55488j2	\([0, -1, 0, -2697, -28215]\)	\(21952/9\)	\(889807343616\)	\([2, 2]\)	\(73728\)	\(0.99039\)
55488.bs4	55488j3	\([0, -1, 0, 8863, -215487]\)	\(97336/81\)	\(-64066128740352\)	\([2]\)	\(147456\)	\(1.3370\)
55488.bs1	55488j4	\([0, -1, 0, -37377, -2767935]\)	\(7301384/3\)	\(2372819582976\)	\([2]\)	\(147456\)	\(1.3370\)