Elliptic curve isogeny class with LMFDB label 567.a (Cremona label 567b)

• Label: 567.a
• Number of curves: $1$
• Conductor: $567$
• CM: no
• Rank: $1$

Rank

The elliptic curve 567.a1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 567.a do not have complex multiplication.

Modular form 567.2.a.a

Isogeny graph

Elliptic curves in class 567.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
567.a1	567b1	\([1, -1, 1, -2, 82]\)	\(-9/49\)	\(-2893401\)	\([]\)	\(72\)	\(-0.081246\)	\(\Gamma_0(N)\)-optimal