Elliptic curve isogeny class with Cremona label 172197j (LMFDB label 172197.j)

• Label: 172197j
• Number of curves: $1$
• Conductor: $172197$
• CM: no
• Rank: $1$

Rank

The elliptic curve 172197j1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(19\)	\(1\)
\(53\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 172197j do not have complex multiplication.

Modular form 172197.2.a.j

Elliptic curves in class 172197j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
172197.j1	172197j1	\([0, 0, 1, 198189, -19398967]\)	\(25102282752/19266931\)	\(-660787282691622819\)	\([]\)	\(3179520\)	\(2.1074\)	\(\Gamma_0(N)\)-optimal