Elliptic curve isogeny class with Cremona label 9800k (LMFDB label 9800.i)

• Label: 9800k
• Number of curves: $2$
• Conductor: $9800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 9800k have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9800k do not have complex multiplication.

Modular form 9800.2.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 Cremona numbering.

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

Isogeny graph

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

Elliptic curves in class 9800k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9800.i2	9800k1	\([0, 1, 0, 992, 13488]\)	\(19652/25\)	\(-137200000000\)	\([2]\)	\(9216\)	\(0.82304\)	\(\Gamma_0(N)\)-optimal
9800.i1	9800k2	\([0, 1, 0, -6008, 125488]\)	\(2185454/625\)	\(6860000000000\)	\([2]\)	\(18432\)	\(1.1696\)