Elliptic curve isogeny class with LMFDB label 106470.cn (Cremona label 106470r)

• Label: 106470.cn
• Number of curves: $1$
• Conductor: $106470$
• CM: no
• Rank: $1$

Rank

The elliptic curve 106470.cn1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 106470.cn do not have complex multiplication.

Modular form 106470.2.a.cn

Elliptic curves in class 106470.cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
106470.cn1	106470r1	\([1, -1, 0, -1588209, 1371548465]\)	\(-788101442546067/988663371500\)	\(-555793094054798554500\)	\([]\)	\(4942080\)	\(2.6739\)	\(\Gamma_0(N)\)-optimal