Elliptic curve isogeny class with LMFDB label 140429.a (Cremona label 140429a)

• Label: 140429.a
• Number of curves: $1$
• Conductor: $140429$
• CM: no
• Rank: $1$

Rank

The elliptic curve 140429.a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(19\)	\(1\)
\(389\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + 5 T + 7 T^{2}\)	1.7.f
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 140429.a do not have complex multiplication.

Modular form 140429.2.a.a

Elliptic curves in class 140429.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
140429.a1	140429a1	\([0, -1, 1, -842, -6515]\)	\(1404928/389\)	\(18300847709\)	\([]\)	\(270000\)	\(0.67658\)	\(\Gamma_0(N)\)-optimal