Elliptic curve isogeny class with Cremona label 171549c (LMFDB label 171549.c)

• Label: 171549c
• Number of curves: $1$
• Conductor: $171549$
• CM: no
• Rank: $1$

Rank

The elliptic curve 171549c1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1\)
\(389\)	\(1 + T\)

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.d
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 171549c do not have complex multiplication.

Modular form 171549.2.a.c

Elliptic curves in class 171549c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
171549.c1	171549c1	\([0, 0, 1, -1029, 9175]\)	\(1404928/389\)	\(33363021069\)	\([]\)	\(224640\)	\(0.72662\)	\(\Gamma_0(N)\)-optimal