Elliptic curve isogeny class with LMFDB label 300352.w (Cremona label 300352w)

• Label: 300352.w
• Number of curves: $1$
• Conductor: $300352$
• CM: no
• Rank: $1$

Rank

The elliptic curve 300352.w1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(13\)	\(1 - T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 300352.w do not have complex multiplication.

Modular form 300352.2.a.w

Elliptic curves in class 300352.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
300352.w1	300352w1	\([0, -1, 0, -6608225, -6536255999]\)	\(-934165699635529/21632\)	\(-739011165421568\)	\([]\)	\(7741440\)	\(2.3757\)	\(\Gamma_0(N)\)-optimal