Elliptic curve isogeny class with LMFDB label 9600.j (Cremona label 9600bs)

• Label: 9600.j
• Number of curves: $2$
• Conductor: $9600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 9600.j have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9600.j do not have complex multiplication.

Modular form 9600.2.a.j

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 9600.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9600.j1	9600bs2	\([0, -1, 0, -41833, 2956537]\)	\(506024032/59049\)	\(944784000000000\)	\([2]\)	\(38400\)	\(1.6051\)
9600.j2	9600bs1	\([0, -1, 0, -40583, 3160287]\)	\(14784166784/243\)	\(121500000000\)	\([2]\)	\(19200\)	\(1.2586\)	\(\Gamma_0(N)\)-optimal