Elliptic curve isogeny class with LMFDB label 167400.k (Cremona label 167400d)

• Label: 167400.k
• Number of curves: $1$
• Conductor: $167400$
• CM: no
• Rank: $1$

Rank

The elliptic curve 167400.k1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(31\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 167400.k do not have complex multiplication.

Modular form 167400.2.a.k

Elliptic curves in class 167400.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
167400.k1	167400d1	\([0, 0, 0, -150, 125]\)	\(55296/31\)	\(209250000\)	\([]\)	\(36864\)	\(0.28677\)	\(\Gamma_0(N)\)-optimal