Elliptic curve isogeny class with Cremona label 163370f (LMFDB label 163370.q)

• Label: 163370f
• Number of curves: $1$
• Conductor: $163370$
• CM: no
• Rank: $1$

Rank

The elliptic curve 163370f1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1 - T\)
\(17\)	\(1 - T\)
\(31\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 163370f do not have complex multiplication.

Modular form 163370.2.a.f

Elliptic curves in class 163370f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
163370.q1	163370f1	\([1, -1, 1, -1409487, 644594849]\)	\(-363089003841/106250\)	\(-90619672728106250\)	\([]\)	\(2083200\)	\(2.2331\)	\(\Gamma_0(N)\)-optimal