Elliptic curve isogeny class with LMFDB label 55488.eb (Cremona label 55488ds)

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

Rank

The elliptic curves in class 55488.eb 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.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 55488.2.a.eb

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 55488.eb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55488.eb1	55488ds4	\([0, 1, 0, -390164257, 2880370652255]\)	\(211293405175481/6973568802\)	\(216788032771826187395137536\)	\([2]\)	\(20889600\)	\(3.8266\)
55488.eb2	55488ds3	\([0, 1, 0, -387019937, 2930411247327]\)	\(206226044828441/236196\)	\(7342648741615478243328\)	\([2]\)	\(10444800\)	\(3.4800\)
55488.eb3	55488ds2	\([0, 1, 0, -53722017, -151574495265]\)	\(551569744601/2592\)	\(80577763968345440256\)	\([2]\)	\(4177920\)	\(3.0219\)
55488.eb4	55488ds1	\([0, 1, 0, -3412897, -2287212577]\)	\(141420761/9216\)	\(286498716331894898688\)	\([2]\)	\(2088960\)	\(2.6753\)	\(\Gamma_0(N)\)-optimal