Cremona's table of elliptic curves

549 = 3² · 61

Field	Data	Notes
Atkin-Lehner	3+ 61+	Signs for the Atkin-Lehner involutions
Class	549a	Isogeny class
Conductor	549	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	100467 = 33 · 612	Discriminant
Eigenvalues	1 3+  0 -2 -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-12,9]	[a1,a2,a3,a4,a6]
Generators	[0:3:1]	Generators of the group modulo torsion
j	7414875/3721	j-invariant
L	2.3235893668019	L(r)(E,1)/r!
Ω	2.9764069064814	Real period
R	0.7806692565261	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8784g2 35136e2 549b2 13725b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 549a2

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	+	0	-2	-4	-2	2	-4	0	6	-6	2	4	-2	-4	-6	12	+	-10	8	10	-6	-4	-2	-2

---

Quadratic twists for elliptic curve 549a2

-4	8	-3	5	-7	-11	13	61
8784g2	35136e2	549b2	13725b2	26901g2	66429b2	92781b2	33489d2

---

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