Elliptic curve isogeny class with Cremona label 11466ca (LMFDB label 11466.ck)

• Label: 11466ca
• Number of curves: $2$
• Conductor: $11466$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 11466ca have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 11466ca do not have complex multiplication.

Modular form 11466.2.a.ca

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 11466ca

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11466.ck1	11466ca1	\([1, -1, 1, -528674, 34092321]\)	\(65352943209688399/35827476332544\)	\(8958552974523629568\)	\([2]\)	\(299520\)	\(2.3273\)	\(\Gamma_0(N)\)-optimal
11466.ck2	11466ca2	\([1, -1, 1, 2051806, 267367713]\)	\(3820420340137317041/2334869460099072\)	\(-583827103889392656384\)	\([2]\)	\(599040\)	\(2.6739\)