Elliptic curve isogeny class with LMFDB label 160688.p (Cremona label 160688p)

• Label: 160688.p
• Number of curves: $1$
• Conductor: $160688$
• CM: no
• Rank: $0$

Rank

The elliptic curve 160688.p1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1\)
\(83\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 160688.p do not have complex multiplication.

Modular form 160688.2.a.p

Elliptic curves in class 160688.p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
160688.p1	160688p1	\([0, 0, 0, -847, 13310]\)	\(-148176/83\)	\(-37642128128\)	\([]\)	\(432000\)	\(0.73256\)	\(\Gamma_0(N)\)-optimal