Elliptic curve isogeny class with Cremona label 8330w (LMFDB label 8330.ba)

• Label: 8330w
• Number of curves: $1$
• Conductor: $8330$
• CM: no
• Rank: $0$

Rank

The elliptic curve 8330w1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8330w do not have complex multiplication.

Modular form 8330.2.a.w

Elliptic curves in class 8330w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8330.ba1	8330w1	\([1, -1, 1, 603, 1789]\)	\(206425071/133280\)	\(-15680258720\)	\([]\)	\(11520\)	\(0.64522\)	\(\Gamma_0(N)\)-optimal