Elliptic curve isogeny class with LMFDB label 266256.cn (Cremona label 266256cn)

• Label: 266256.cn
• Number of curves: $2$
• Conductor: $266256$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 266256.cn have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(43\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 266256.cn do not have complex multiplication.

Modular form 266256.2.a.cn

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 266256.cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
266256.cn1	266256cn2	\([0, 0, 0, -22059, 1261018]\)	\(135005697/2\)	\(17585676288\)	\([2]\)	\(337920\)	\(1.1033\)
266256.cn2	266256cn1	\([0, 0, 0, -1419, 18490]\)	\(35937/4\)	\(35171352576\)	\([2]\)	\(168960\)	\(0.75670\)	\(\Gamma_0(N)\)-optimal