Elliptic curve isogeny class with LMFDB label 9600.r (Cremona label 9600i)

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

Rank

The elliptic curves in class 9600.r 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 9600.2.a.r

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.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9600.r1	9600i2	\([0, -1, 0, -6493, 203557]\)	\(14784166784/243\)	\(497664000\)	\([2]\)	\(7680\)	\(0.80043\)
9600.r2	9600i1	\([0, -1, 0, -418, 3082]\)	\(506024032/59049\)	\(944784000\)	\([2]\)	\(3840\)	\(0.45386\)	\(\Gamma_0(N)\)-optimal