Elliptic curve isogeny class with Cremona label 9408bb (LMFDB label 9408.co)

• Label: 9408bb
• Number of curves: $4$
• Conductor: $9408$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 9408bb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 8 T + 17 T^{2}\)	1.17.ai
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9408bb do not have complex multiplication.

Modular form 9408.2.a.bb

Isogeny matrix

The \(i,j\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 9408bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9408.co4	9408bb1	\([0, 1, 0, 1307, 6635]\)	\(2048000/1323\)	\(-159385218048\)	\([2]\)	\(9216\)	\(0.83846\)	\(\Gamma_0(N)\)-optimal
9408.co3	9408bb2	\([0, 1, 0, -5553, 49167]\)	\(9826000/5103\)	\(9836344885248\)	\([2]\)	\(18432\)	\(1.1850\)
9408.co2	9408bb3	\([0, 1, 0, -22213, 1304939]\)	\(-10061824000/352947\)	\(-42520434281472\)	\([2]\)	\(27648\)	\(1.3878\)
9408.co1	9408bb4	\([0, 1, 0, -358353, 82449135]\)	\(2640279346000/3087\)	\(5950381473792\)	\([2]\)	\(55296\)	\(1.7343\)