Elliptic curve isogeny class with LMFDB label 574.b (Cremona label 574a)

• Label: 574.b
• Number of curves: $1$
• Conductor: $574$
• CM: no
• Rank: $1$

Rank

The elliptic curve 574.b1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(7\)	\(1 + T\)
\(41\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 574.b do not have complex multiplication.

Modular form 574.2.a.b

Elliptic curves in class 574.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
574.b1	574a1	\([1, 1, 0, -2, -2]\)	\(1771561/574\)	\(574\)	\([]\)	\(24\)	\(-0.76726\)	\(\Gamma_0(N)\)-optimal