Elliptic curve isogeny class with LMFDB label 9408.bt (Cremona label 9408cn)

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

Rank

The elliptic curve 9408.bt1 has 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 9408.2.a.bt

Elliptic curves in class 9408.bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9408.bt1	9408cn1	\([0, 1, 0, -14177, -663489]\)	\(-1668296/27\)	\(-5100326977536\)	\([]\)	\(24192\)	\(1.2388\)	\(\Gamma_0(N)\)-optimal