Elliptic curve isogeny class with Cremona label 13200cm (LMFDB label 13200.bo)

• Label: 13200cm
• Number of curves: $4$
• Conductor: $13200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 13200cm have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 13200.2.a.cm

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 13200cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13200.bo3	13200cm1	\([0, 1, 0, -1033, -17062]\)	\(-488095744/200475\)	\(-50118750000\)	\([2]\)	\(13824\)	\(0.76145\)	\(\Gamma_0(N)\)-optimal
13200.bo2	13200cm2	\([0, 1, 0, -17908, -928312]\)	\(158792223184/16335\)	\(65340000000\)	\([2]\)	\(27648\)	\(1.1080\)
13200.bo4	13200cm3	\([0, 1, 0, 7967, 185438]\)	\(223673040896/187171875\)	\(-46792968750000\)	\([2]\)	\(41472\)	\(1.3108\)
13200.bo1	13200cm4	\([0, 1, 0, -38908, 1591688]\)	\(1628514404944/664335375\)	\(2657341500000000\)	\([2]\)	\(82944\)	\(1.6573\)