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

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

Rank

The elliptic curves in class 266256.u 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.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	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.ae
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 266256.2.a.u

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.u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
266256.u1	266256u2	\([0, 0, 0, -198531, -34047486]\)	\(135005697/2\)	\(12819958013952\)	\([2]\)	\(1013760\)	\(1.6526\)
266256.u2	266256u1	\([0, 0, 0, -12771, -499230]\)	\(35937/4\)	\(25639916027904\)	\([2]\)	\(506880\)	\(1.3060\)	\(\Gamma_0(N)\)-optimal