Elliptic curve isogeny class with Cremona label 172800f (LMFDB label 172800.l)

• Label: 172800f
• Number of curves: $1$
• Conductor: $172800$
• CM: no
• Rank: $1$

Rank

The elliptic curve 172800f1 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 172800f do not have complex multiplication.

Modular form 172800.2.a.f

Elliptic curves in class 172800f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
172800.l1	172800f1	\([0, 0, 0, -1350, -27000]\)	\(-1728\)	\(-157464000000\)	\([]\)	\(186624\)	\(0.85133\)	\(\Gamma_0(N)\)-optimal