Elliptic curve isogeny class with LMFDB label 5280.k (Cremona label 5280f)

• Label: 5280.k
• Number of curves: $4$
• Conductor: $5280$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 5280.k have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5280.k do not have complex multiplication.

Modular form 5280.2.a.k

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 5280.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5280.k1	5280f3	\([0, 1, 0, -2936, 60264]\)	\(5468520153032/22275\)	\(11404800\)	\([4]\)	\(2048\)	\(0.56455\)
5280.k2	5280f2	\([0, 1, 0, -561, -4161]\)	\(4775581504/1098075\)	\(4497715200\)	\([2]\)	\(2048\)	\(0.56455\)
5280.k3	5280f1	\([0, 1, 0, -186, 864]\)	\(11179320256/680625\)	\(43560000\)	\([2, 2]\)	\(1024\)	\(0.21798\)	\(\Gamma_0(N)\)-optimal
5280.k4	5280f4	\([0, 1, 0, 144, 3900]\)	\(640503928/12890625\)	\(-6600000000\)	\([2]\)	\(2048\)	\(0.56455\)