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

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

Rank

The elliptic curves in class 9680.m 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 9680.2.a.m

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.

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

Isogeny graph

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

Elliptic curves in class 9680.m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9680.m1	9680k2	\([0, 0, 0, -177023, -28667078]\)	\(1016339184/25\)	\(15090865222400\)	\([2]\)	\(50688\)	\(1.6382\)
9680.m2	9680k1	\([0, 0, 0, -10648, -483153]\)	\(-3538944/625\)	\(-23579476910000\)	\([2]\)	\(25344\)	\(1.2916\)	\(\Gamma_0(N)\)-optimal