Elliptic curve isogeny class with LMFDB label 47432.h (Cremona label 47432o)

• Label: 47432.h
• Number of curves: $1$
• Conductor: $47432$
• CM: no
• Rank: $1$

Rank

The elliptic curve 47432.h1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 7 T + 23 T^{2}\)	1.23.h
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 47432.h do not have complex multiplication.

Modular form 47432.2.a.h

Elliptic curves in class 47432.h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47432.h1	47432o1	\([0, -1, 0, -1976, -30743]\)	\(12544\)	\(68056287376\)	\([]\)	\(32400\)	\(0.82207\)	\(\Gamma_0(N)\)-optimal