Elliptic curve isogeny class with LMFDB label 9680.f (Cremona label 9680q)

• Label: 9680.f
• Number of curves: $2$
• Conductor: $9680$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 9680.f have rank \(1\).

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
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	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.f do not have complex multiplication.

Modular form 9680.2.a.f

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.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9680.f1	9680q2	\([0, -1, 0, -436, -3364]\)	\(-296587984/125\)	\(-3872000\)	\([]\)	\(1728\)	\(0.22525\)
9680.f2	9680q1	\([0, -1, 0, 4, -20]\)	\(176/5\)	\(-154880\)	\([]\)	\(576\)	\(-0.32406\)	\(\Gamma_0(N)\)-optimal