Elliptic curve isogeny class with Cremona label 166a (LMFDB label 166.a)

• Label: 166a
• Number of curves: $1$
• Conductor: $166$
• CM: no
• Rank: $1$

Rank

The elliptic curve 166a1 has rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$83$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + T + 3 T^{2}$	1.3.b
$5$	$1 + 2 T + 5 T^{2}$	1.5.c
$7$	$1 - T + 7 T^{2}$	1.7.ab
$11$	$1 + 5 T + 11 T^{2}$	1.11.f
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 + 3 T + 17 T^{2}$	1.17.d
$19$	$1 + 2 T + 19 T^{2}$	1.19.c
$23$	$1 - 4 T + 23 T^{2}$	1.23.ae
$29$	$1 + 3 T + 29 T^{2}$	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 166a do not have complex multiplication.

Modular form 166.2.a.a

Elliptic curves in class 166a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
166.a1	166a1	$[1, 1, 0, -6, 4]$	$-30664297/1328$	$-1328$	$[]$	$8$	$-0.63506$	$\Gamma_0(N)$-optimal