Cremona's table of elliptic curves

574 = 2 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2+ 7+ 41+	Signs for the Atkin-Lehner involutions
Class	574a	Isogeny class
Conductor	574	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	574 = 2 · 7 · 41	Discriminant
Eigenvalues	2+ -1  1 7+  0  2 -5 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2,-2]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1]	Generators of the group modulo torsion
j	1771561/574	j-invariant
L	1.4097851799409	L(r)(E,1)/r!
Ω	3.8864860069485	Real period
R	0.36274032054159	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4592j1 18368a1 5166bb1 14350r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 574a1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-1	1	+	0	2	-5	-4	6	-9	3	-8	+	7	-10	-13	-14	-5	4	-15	-6	-3	16	13	17

---

Quadratic twists for elliptic curve 574a1

-4	8	-3	5	-7	-11	13	41
4592j1	18368a1	5166bb1	14350r1	4018e1	69454y1	97006s1	23534k1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations