Elliptic curve isogeny class with LMFDB label 9408.bq (Cremona label 9408bl)

• Label: 9408.bq
• Number of curves: $2$
• Conductor: $9408$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 9408.bq 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 9408.2.a.bq

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 9408.bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9408.bq1	9408bl1	\([0, 1, 0, -18440, -765066]\)	\(92100460096/20253807\)	\(152501768943552\)	\([2]\)	\(46080\)	\(1.4350\)	\(\Gamma_0(N)\)-optimal
9408.bq2	9408bl2	\([0, 1, 0, 41095, -4634841]\)	\(15926924096/28588707\)	\(-13776620707196928\)	\([2]\)	\(92160\)	\(1.7816\)