Elliptic curve isogeny class with LMFDB label 262080.kf (Cremona label 262080kf)

• Label: 262080.kf
• Number of curves: $4$
• Conductor: $262080$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 262080.kf have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(13\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 262080.kf do not have complex multiplication.

Modular form 262080.2.a.kf

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 262080.kf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
262080.kf1	262080kf4	\([0, 0, 0, -9211212, -9875017584]\)	\(16751080718799363/1529437000000\)	\(7891558982221824000000\)	\([2]\)	\(15925248\)	\(2.9408\)
262080.kf2	262080kf2	\([0, 0, 0, -8999052, -10390662896]\)	\(11387025941627437947/10765300\)	\(76195587686400\)	\([2]\)	\(5308416\)	\(2.3915\)
262080.kf3	262080kf3	\([0, 0, 0, -2022732, 933580944]\)	\(177381177331203/29679104000\)	\(153137657684164608000\)	\([2]\)	\(7962624\)	\(2.5943\)
262080.kf4	262080kf1	\([0, 0, 0, -562572, -162274544]\)	\(2781982314427707/2703013040\)	\(19131623559659520\)	\([2]\)	\(2654208\)	\(2.0450\)	\(\Gamma_0(N)\)-optimal