Elliptic curve isogeny class with LMFDB label 4080.p (Cremona label 4080j)

• Label: 4080.p
• Number of curves: $1$
• Conductor: $4080$
• CM: no
• Rank: $1$

Rank

The elliptic curve 4080.p1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4080.p do not have complex multiplication.

Modular form 4080.2.a.p

Elliptic curves in class 4080.p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4080.p1	4080j1	\([0, -1, 0, -2840, -81813]\)	\(-158384129218816/93270234375\)	\(-1492323750000\)	\([]\)	\(6720\)	\(1.0385\)	\(\Gamma_0(N)\)-optimal