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

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

Rank

The elliptic curves in class 266256.cj 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.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 266256.2.a.cj

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.cj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
266256.cj1	266256cj2	\([0, 0, 0, -367083819, 2707013469402]\)	\(135005697/2\)	\(81039608879127599259648\)	\([2]\)	\(43591680\)	\(3.5332\)
266256.cj2	266256cj1	\([0, 0, 0, -23613579, 39692279610]\)	\(35937/4\)	\(162079217758255198519296\)	\([2]\)	\(21795840\)	\(3.1866\)	\(\Gamma_0(N)\)-optimal