Elliptic curve isogeny class with Cremona label 13104k (LMFDB label 13104.ba)

• Label: 13104k
• Number of curves: $2$
• Conductor: $13104$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 13104k have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13104k do not have complex multiplication.

Modular form 13104.2.a.k

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 13104k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13104.ba2	13104k1	\([0, 0, 0, -92910, 11189747]\)	\(-7604375980288000/236743082667\)	\(-2761371316227888\)	\([2]\)	\(61440\)	\(1.7396\)	\(\Gamma_0(N)\)-optimal
13104.ba1	13104k2	\([0, 0, 0, -1497495, 705335654]\)	\(1989996724085074000/1843096437\)	\(343966029458688\)	\([2]\)	\(122880\)	\(2.0862\)