Elliptic curve isogeny class with LMFDB label 128700.cd (Cremona label 128700w)

• Label: 128700.cd
• Number of curves: $1$
• Conductor: $128700$
• CM: no
• Rank: $0$

Rank

The elliptic curve 128700.cd1 has rank \(0\).

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
\(17\)	\( 1 - 8 T + 17 T^{2}\)	1.17.ai
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 128700.2.a.cd

Elliptic curves in class 128700.cd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
128700.cd1	128700w1	\([0, 0, 0, 12195, 254745]\)	\(687830780160/494190983\)	\(-144106090642800\)	\([]\)	\(380160\)	\(1.4052\)	\(\Gamma_0(N)\)-optimal