Elliptic curve isogeny class with Cremona label 26460n (LMFDB label 26460.be)

• Label: 26460n
• Number of curves: $2$
• Conductor: $26460$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 26460n have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 26460n do not have complex multiplication.

Modular form 26460.2.a.n

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 26460n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26460.be2	26460n1	\([0, 0, 0, -567, -4914]\)	\(81648/5\)	\(1234517760\)	\([]\)	\(11664\)	\(0.49648\)	\(\Gamma_0(N)\)-optimal
26460.be1	26460n2	\([0, 0, 0, -8127, 280854]\)	\(26714352/125\)	\(277766496000\)	\([]\)	\(34992\)	\(1.0458\)