Elliptic curve isogeny class with LMFDB label 13200.p (Cremona label 13200a)

• Label: 13200.p
• Number of curves: $4$
• Conductor: $13200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 13200.p have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13200.p do not have complex multiplication.

Modular form 13200.2.a.p

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 13200.p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13200.p1	13200a3	\([0, -1, 0, -11808, -489888]\)	\(5690357426/891\)	\(28512000000\)	\([2]\)	\(16384\)	\(1.0171\)
13200.p2	13200a2	\([0, -1, 0, -808, -5888]\)	\(3650692/1089\)	\(17424000000\)	\([2, 2]\)	\(8192\)	\(0.67056\)
13200.p3	13200a1	\([0, -1, 0, -308, 2112]\)	\(810448/33\)	\(132000000\)	\([2]\)	\(4096\)	\(0.32398\)	\(\Gamma_0(N)\)-optimal
13200.p4	13200a4	\([0, -1, 0, 2192, -41888]\)	\(36382894/43923\)	\(-1405536000000\)	\([2]\)	\(16384\)	\(1.0171\)