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

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

Rank

The elliptic curves in class 26460r 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 26460.2.a.r

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 26460r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26460.r1	26460r1	\([0, 0, 0, -31752, -2185596]\)	\(-5971968/25\)	\(-14820385708800\)	\([]\)	\(81648\)	\(1.3822\)	\(\Gamma_0(N)\)-optimal
26460.r2	26460r2	\([0, 0, 0, 74088, -11520684]\)	\(8429568/15625\)	\(-83364669612000000\)	\([]\)	\(244944\)	\(1.9315\)