Elliptic curve isogeny class with LMFDB label 86400.g (Cremona label 86400n)

• Label: 86400.g
• Number of curves: $1$
• Conductor: $86400$
• CM: no
• Rank: $1$

Rank

The elliptic curve 86400.g1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 86400.g do not have complex multiplication.

Modular form 86400.2.a.g

Elliptic curves in class 86400.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
86400.g1	86400n1	\([0, 0, 0, 75, 750]\)	\(864/5\)	\(-270000000\)	\([]\)	\(23040\)	\(0.29979\)	\(\Gamma_0(N)\)-optimal