Elliptic curve isogeny class with Cremona label 128700bz (LMFDB label 128700.q)

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

Rank

The elliptic curve 128700bz1 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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 128700.2.a.bz

Elliptic curves in class 128700bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
128700.q1	128700bz1	\([0, 0, 0, -2109000, 1178862500]\)	\(-2846137769984/1287\)	\(-469111500000000\)	\([]\)	\(1489920\)	\(2.1549\)	\(\Gamma_0(N)\)-optimal