Elliptic curve isogeny class with LMFDB label 9600.bf (Cremona label 9600w)

• Label: 9600.bf
• Number of curves: $2$
• Conductor: $9600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 9600.bf have rank \(0\).

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

See L-function page for more information

Complex multiplication

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

Modular form 9600.2.a.bf

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.bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9600.bf1	9600w1	\([0, 1, 0, -158, 438]\)	\(219488/75\)	\(150000000\)	\([2]\)	\(4608\)	\(0.27086\)	\(\Gamma_0(N)\)-optimal
9600.bf2	9600w2	\([0, 1, 0, 467, 3563]\)	\(43904/45\)	\(-11520000000\)	\([2]\)	\(9216\)	\(0.61744\)