Elliptic curve isogeny class with Cremona label 13440ck (LMFDB label 13440.cf)

• Label: 13440ck
• Number of curves: $2$
• Conductor: $13440$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 13440ck have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13440ck do not have complex multiplication.

Modular form 13440.2.a.ck

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 13440ck

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13440.cf2	13440ck1	\([0, 1, 0, -14355, 1361853]\)	\(-1277978627383936/2412172153125\)	\(-617516071200000\)	\([2]\)	\(61440\)	\(1.5279\)	\(\Gamma_0(N)\)-optimal
13440.cf1	13440ck2	\([0, 1, 0, -292185, 60650775]\)	\(336751085874643808/271318359375\)	\(2222640000000000\)	\([2]\)	\(122880\)	\(1.8745\)