Elliptic curve isogeny class with Cremona label 1430k (LMFDB label 1430.e)

• Label: 1430k
• Number of curves: $1$
• Conductor: $1430$
• CM: no
• Rank: $1$

Rank

The elliptic curve 1430k1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 - T\)
\(11\)	\(1 - T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 3 T + 3 T^{2}\)	1.3.ad
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1430k do not have complex multiplication.

Modular form 1430.2.a.k

Elliptic curves in class 1430k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1430.e1	1430k1	\([1, -1, 1, -3057, 133281]\)	\(-3158470573163361/5758438400000\)	\(-5758438400000\)	\([]\)	\(6240\)	\(1.1386\)	\(\Gamma_0(N)\)-optimal