Elliptic curve isogeny class with LMFDB label 281775.q (Cremona label 281775q)

• Label: 281775.q
• Number of curves: $1$
• Conductor: $281775$
• CM: no
• Rank: $1$

Rank

The elliptic curve 281775.q1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(13\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 281775.q do not have complex multiplication.

Modular form 281775.2.a.q

Elliptic curves in class 281775.q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
281775.q1	281775q1	\([1, 0, 0, -328888, -75538483]\)	\(-417267265/19773\)	\(-186434434311328125\)	\([]\)	\(3444480\)	\(2.0766\)	\(\Gamma_0(N)\)-optimal