Elliptic curve isogeny class with Cremona label 13552q (LMFDB label 13552.y)

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

Rank

The elliptic curves in class 13552q 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 \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 13552.2.a.q

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 13552q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13552.y1	13552q1	\([0, -1, 0, -10204, -401124]\)	\(-2141392/49\)	\(-2688917803264\)	\([]\)	\(31680\)	\(1.1726\)	\(\Gamma_0(N)\)-optimal
13552.y2	13552q2	\([0, -1, 0, 43036, -1785364]\)	\(160630448/117649\)	\(-6456091645636864\)	\([]\)	\(95040\)	\(1.7220\)