Elliptic curve isogeny class with LMFDB label 47600.bm (Cremona label 47600b)

• Label: 47600.bm
• Number of curves: $1$
• Conductor: $47600$
• CM: no
• Rank: $1$

Rank

The elliptic curve 47600.bm1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 47600.bm do not have complex multiplication.

Modular form 47600.2.a.bm

Elliptic curves in class 47600.bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47600.bm1	47600b1	\([0, -1, 0, -8, 47]\)	\(-160000/2023\)	\(-809200\)	\([]\)	\(7296\)	\(-0.18462\)	\(\Gamma_0(N)\)-optimal