Elliptic curve isogeny class with Cremona label 267589a (LMFDB label 267589.a)

• Label: 267589a
• Number of curves: $1$
• Conductor: $267589$
• CM: no
• Rank: $0$

Rank

The elliptic curve 267589a1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(7\)	\(1\)
\(43\)	\(1 + T\)
\(127\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 267589a do not have complex multiplication.

Modular form 267589.2.a.a

Elliptic curves in class 267589a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
267589.a1	267589a1	\([0, 1, 1, -800, 8362]\)	\(481890304/5461\)	\(642481189\)	\([]\)	\(140616\)	\(0.50353\)	\(\Gamma_0(N)\)-optimal