Elliptic curve isogeny class with LMFDB label 397488.bz (Cremona label 397488bz)

• Label: 397488.bz
• Number of curves: $1$
• Conductor: $397488$
• CM: no
• Rank: $0$

Rank

The elliptic curve 397488.bz1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 397488.bz do not have complex multiplication.

Modular form 397488.2.a.bz

Elliptic curves in class 397488.bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
397488.bz1	397488bz1	\([0, -1, 0, -1486, -12221]\)	\(23296/9\)	\(140292197136\)	\([]\)	\(338688\)	\(0.83789\)	\(\Gamma_0(N)\)-optimal