Elliptic curve isogeny class with Cremona label 9600e (LMFDB label 9600.x)

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

Rank

The elliptic curves in class 9600e 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 9600.2.a.e

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 9600e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9600.x1	9600e1	\([0, -1, 0, -208258, -36511238]\)	\(499460194376672/253125\)	\(506250000000\)	\([2]\)	\(46080\)	\(1.5787\)	\(\Gamma_0(N)\)-optimal
9600.x2	9600e2	\([0, -1, 0, -207133, -36926363]\)	\(-3839138053504/87890625\)	\(-22500000000000000\)	\([2]\)	\(92160\)	\(1.9253\)