Elliptic curve isogeny class with LMFDB label 13552.j (Cremona label 13552n)

• Label: 13552.j
• Number of curves: $2$
• Conductor: $13552$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 13552.j have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13552.j do not have complex multiplication.

Modular form 13552.2.a.j

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 13552.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13552.j1	13552n2	\([0, 0, 0, -908347, 333215850]\)	\(11422548526761/4312\)	\(31289225347072\)	\([2]\)	\(138240\)	\(1.9401\)
13552.j2	13552n1	\([0, 0, 0, -56507, 5257450]\)	\(-2749884201/54208\)	\(-393350261506048\)	\([2]\)	\(69120\)	\(1.5935\)	\(\Gamma_0(N)\)-optimal