Elliptic curve isogeny class with Cremona label 198198da (LMFDB label 198198.v)

• Label: 198198da
• Number of curves: $1$
• Conductor: $198198$
• CM: no
• Rank: $1$

Rank

The elliptic curve 198198da1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 198198da do not have complex multiplication.

Modular form 198198.2.a.da

Elliptic curves in class 198198da

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
198198.v1	198198da1	\([1, -1, 0, -8190, -325836]\)	\(-47045881/8736\)	\(-11282264177184\)	\([]\)	\(432000\)	\(1.2290\)	\(\Gamma_0(N)\)-optimal