Elliptic curve isogeny class with LMFDB label 9800.bj (Cremona label 9800bg)

• Label: 9800.bj
• Number of curves: $2$
• Conductor: $9800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 9800.bj have rank \(1\).

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.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 9800.2.a.bj

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 9800.bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9800.bj1	9800bg2	\([0, -1, 0, -49408, 4192812]\)	\(3543122/49\)	\(184473632000000\)	\([2]\)	\(30720\)	\(1.5430\)
9800.bj2	9800bg1	\([0, -1, 0, -408, 174812]\)	\(-4/7\)	\(-13176688000000\)	\([2]\)	\(15360\)	\(1.1964\)	\(\Gamma_0(N)\)-optimal