Elliptic curve isogeny class with Cremona label 198550cc (LMFDB label 198550.k)

• Label: 198550cc
• Number of curves: $1$
• Conductor: $198550$
• CM: no
• Rank: $1$

Rank

The elliptic curve 198550cc1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 198550cc do not have complex multiplication.

Modular form 198550.2.a.cc

Elliptic curves in class 198550cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
198550.k1	198550cc1	\([1, 1, 0, 50, 350]\)	\(59375/242\)	\(-54601250\)	\([]\)	\(59616\)	\(0.16728\)	\(\Gamma_0(N)\)-optimal