Elliptic curve isogeny class with Cremona label 266418q (LMFDB label 266418.q)

• Label: 266418q
• Number of curves: $2$
• Conductor: $266418$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 266418q have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(19\)	\(1\)
\(41\)	\(1 + T\)

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
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 266418q do not have complex multiplication.

Modular form 266418.2.a.q

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 266418q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
266418.q1	266418q1	\([1, -1, 0, -216126, 38508372]\)	\(32553430057/212544\)	\(7289504084091456\)	\([2]\)	\(2322432\)	\(1.8797\)	\(\Gamma_0(N)\)-optimal
266418.q2	266418q2	\([1, -1, 0, -86166, 84280284]\)	\(-2062933417/88232328\)	\(-3026055382908465672\)	\([2]\)	\(4644864\)	\(2.2262\)