Elliptic curve isogeny class with Cremona label 198744bp (LMFDB label 198744.r)

• Label: 198744bp
• Number of curves: $1$
• Conductor: $198744$
• CM: no
• Rank: $1$

Rank

The elliptic curve 198744bp1 has rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 198744.2.a.bp

Elliptic curves in class 198744bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
198744.r1	198744bp1	\([0, -1, 0, 6704, 475084]\)	\(68782/243\)	\(-117704324634624\)	\([]\)	\(518400\)	\(1.3829\)	\(\Gamma_0(N)\)-optimal