Elliptic curve isogeny class with LMFDB label 10043.b (Cremona label 10043c)

• Label: 10043.b
• Number of curves: $1$
• Conductor: $10043$
• CM: no
• Rank: $1$

Rank

The elliptic curve 10043.b1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(11\)	\(1\)
\(83\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 10043.b do not have complex multiplication.

Modular form 10043.2.a.b

Elliptic curves in class 10043.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10043.b1	10043c1	\([1, 1, 0, 119, 356]\)	\(103823/83\)	\(-147039563\)	\([]\)	\(2700\)	\(0.25508\)	\(\Gamma_0(N)\)-optimal