Elliptic curve isogeny class with LMFDB label 9680.k (Cremona label 9680bb)

• Label: 9680.k
• Number of curves: $2$
• Conductor: $9680$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 9680.k have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9680.k do not have complex multiplication.

Modular form 9680.2.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.

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

Isogeny graph

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

Elliptic curves in class 9680.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9680.k1	9680bb1	\([0, -1, 0, -1176160, 499304192]\)	\(-1693700041/32000\)	\(-3399670117302272000\)	\([]\)	\(152064\)	\(2.3505\)	\(\Gamma_0(N)\)-optimal
9680.k2	9680bb2	\([0, -1, 0, 4680240, 2331186112]\)	\(106718863559/83886080\)	\(-8912031232300867911680\)	\([]\)	\(456192\)	\(2.8998\)