Elliptic curve isogeny class with LMFDB label 129600.bg (Cremona label 129600ic)

• Label: 129600.bg
• Number of curves: $1$
• Conductor: $129600$
• CM: no
• Rank: $1$

Rank

The elliptic curve 129600.bg1 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
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	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 129600.bg do not have complex multiplication.

Modular form 129600.2.a.bg

Elliptic curves in class 129600.bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
129600.bg1	129600ic1	\([0, 0, 0, -67500, 6210000]\)	\(11250\)	\(3023308800000000\)	\([]\)	\(691200\)	\(1.7104\)	\(\Gamma_0(N)\)-optimal