Elliptic curve isogeny class with LMFDB label 199920.cp (Cremona label 199920go)

• Label: 199920.cp
• Number of curves: $1$
• Conductor: $199920$
• CM: no
• Rank: $0$

Rank

The elliptic curve 199920.cp1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 199920.cp do not have complex multiplication.

Modular form 199920.2.a.cp

Elliptic curves in class 199920.cp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
199920.cp1	199920go1	\([0, -1, 0, 374540, -435984233]\)	\(3086803246205696/45384521484375\)	\(-85431097089843750000\)	\([]\)	\(5765760\)	\(2.5052\)	\(\Gamma_0(N)\)-optimal