Elliptic curve isogeny class with Cremona label 266560gy (LMFDB label 266560.gy)

• Label: 266560gy
• Number of curves: $2$
• Conductor: $266560$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 266560gy have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 266560gy do not have complex multiplication.

Modular form 266560.2.a.gy

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 266560gy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
266560.gy1	266560gy1	\([0, -1, 0, -23585, 1215425]\)	\(47045881/6800\)	\(209718660300800\)	\([2]\)	\(1105920\)	\(1.4734\)	\(\Gamma_0(N)\)-optimal
266560.gy2	266560gy2	\([0, -1, 0, 39135, 6521537]\)	\(214921799/722500\)	\(-22282607656960000\)	\([2]\)	\(2211840\)	\(1.8200\)