Elliptic curve isogeny class with LMFDB label 66300.w (Cremona label 66300x)

• Label: 66300.w
• Number of curves: $1$
• Conductor: $66300$
• CM: no
• Rank: $2$

Rank

The elliptic curve 66300.w1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(13\)	\(1 + T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 66300.w do not have complex multiplication.

Modular form 66300.2.a.w

Elliptic curves in class 66300.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
66300.w1	66300x1	\([0, 1, 0, 15742, 82113]\)	\(1725582942464/1008810855\)	\(-252202713750000\)	\([]\)	\(241920\)	\(1.4529\)	\(\Gamma_0(N)\)-optimal