Elliptic curve isogeny class with LMFDB label 198744.j (Cremona label 198744bm)

• Label: 198744.j
• Number of curves: $1$
• Conductor: $198744$
• CM: no
• Rank: $0$

Rank

The elliptic curve 198744.j1 has rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 198744.j do not have complex multiplication.

Modular form 198744.2.a.j

Elliptic curves in class 198744.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
198744.j1	198744bm1	\([0, -1, 0, -9939388944, 382801519911420]\)	\(-3811170500576969572/16129443546333\)	\(-459582809172161645237726204928\)	\([]\)	\(397393920\)	\(4.5462\)	\(\Gamma_0(N)\)-optimal