Elliptic curve isogeny class with Cremona label 165165i (LMFDB label 165165.a)

• Label: 165165i
• Number of curves: $1$
• Conductor: $165165$
• CM: no
• Rank: $1$

Rank

The elliptic curve 165165i1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 165165i do not have complex multiplication.

Modular form 165165.2.a.i

Elliptic curves in class 165165i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
165165.a1	165165i1	\([0, -1, 1, -106036, -13279608]\)	\(-9005691727335424/19464046875\)	\(-284973110296875\)	\([]\)	\(1161216\)	\(1.6576\)	\(\Gamma_0(N)\)-optimal