Elliptic curve isogeny class with Cremona label 128700bu (LMFDB label 128700.f)

• Label: 128700bu
• Number of curves: $1$
• Conductor: $128700$
• CM: no
• Rank: $1$

Rank

The elliptic curve 128700bu1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 128700bu do not have complex multiplication.

Modular form 128700.2.a.bu

Elliptic curves in class 128700bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
128700.f1	128700bu1	\([0, 0, 0, -143625, 45948125]\)	\(-71912815360/158559687\)	\(-722437573893750000\)	\([]\)	\(1382400\)	\(2.1155\)	\(\Gamma_0(N)\)-optimal