Elliptic curve isogeny class with LMFDB label 47040.fd (Cremona label 47040gd)

• Label: 47040.fd
• Number of curves: $1$
• Conductor: $47040$
• CM: no
• Rank: $0$

Rank

The elliptic curve 47040.fd1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 - 5 T + 23 T^{2}\)	1.23.af
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 47040.fd do not have complex multiplication.

Modular form 47040.2.a.fd

Isogeny graph

Elliptic curves in class 47040.fd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47040.fd1	47040gd1	\([0, 1, 0, 159, -225]\)	\(68782/45\)	\(-289013760\)	\([]\)	\(15360\)	\(0.31234\)	\(\Gamma_0(N)\)-optimal