Elliptic curve isogeny class with Cremona label 172062c (LMFDB label 172062.bc)

• Label: 172062c
• Number of curves: $1$
• Conductor: $172062$
• CM: no
• Rank: $1$

Rank

The elliptic curve 172062c1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(11\)	\(1\)
\(79\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 5 T + 23 T^{2}\)	1.23.af
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 172062c do not have complex multiplication.

Modular form 172062.2.a.c

Elliptic curves in class 172062c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
172062.bc1	172062c1	\([1, -1, 1, -196241, 32656385]\)	\(9474973054156753/276038731008\)	\(24349100423484672\)	\([]\)	\(2967552\)	\(1.9219\)	\(\Gamma_0(N)\)-optimal