Elliptic curve isogeny class with LMFDB label 26569.a (Cremona label 26569a)

• Label: 26569.a
• Number of curves: $2$
• Conductor: $26569$
• CM: \(\Q(\sqrt{-163}) \)
• Rank: $1$

Rank

The elliptic curves in class 26569.a have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(163\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 26569.a has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-163}) \).

Modular form 26569.2.a.a

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.

\(\left(\begin{array}{rr} 1 & 163 \\ 163 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 26569.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
26569.a1	26569a2	\([0, 0, 1, -57772164980, -5344733777551611]\)	\(-262537412640768000\)	\(-81224760533853742723\)	\([]\)	\(9676984\)	\(4.3980\)		\(-163\)
26569.a2	26569a1	\([0, 0, 1, -2174420, 1234136692]\)	\(-262537412640768000\)	\(-4330747\)	\([]\)	\(59368\)	\(1.8511\)	\(\Gamma_0(N)\)-optimal	\(-163\)