Elliptic curve isogeny class with LMFDB label 1638.r (Cremona label 1638p)

• Label: 1638.r
• Number of curves: $1$
• Conductor: $1638$
• CM: no
• Rank: $0$

Rank

The elliptic curve 1638.r1 has rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1638.r do not have complex multiplication.

Modular form 1638.2.a.r

Elliptic curves in class 1638.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1638.r1	1638p1	\([1, -1, 1, -977, 12147]\)	\(-141339344329/2167074\)	\(-1579796946\)	\([]\)	\(960\)	\(0.56748\)	\(\Gamma_0(N)\)-optimal