Elliptic curve isogeny class with LMFDB label 9680.l (Cremona label 9680ba)

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

Rank

The elliptic curves in class 9680.l 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.ab
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 9680.2.a.l

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.l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9680.l1	9680ba1	\([0, -1, 0, -9720, -371600]\)	\(-1693700041/32000\)	\(-1919025152000\)	\([]\)	\(13824\)	\(1.1515\)	\(\Gamma_0(N)\)-optimal
9680.l2	9680ba2	\([0, -1, 0, 38680, -1765520]\)	\(106718863559/83886080\)	\(-5030609294458880\)	\([]\)	\(41472\)	\(1.7008\)