Elliptic curve isogeny class with LMFDB label 26208.k (Cremona label 26208m)

• Label: 26208.k
• Number of curves: $2$
• Conductor: $26208$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 26208.k have rank \(1\).

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
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 26208.k do not have complex multiplication.

Modular form 26208.2.a.k

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 26208.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26208.k1	26208m2	\([0, 0, 0, -738156, 244101440]\)	\(14896378491692608/138411\)	\(413293031424\)	\([2]\)	\(122880\)	\(1.8094\)
26208.k2	26208m1	\([0, 0, 0, -46101, 3819944]\)	\(-232245467895232/709540923\)	\(-33104341303488\)	\([2]\)	\(61440\)	\(1.4629\)	\(\Gamma_0(N)\)-optimal