Cremona's table of elliptic curves

549 = 3² · 61

Field	Data	Notes
Atkin-Lehner	3+ 61+	Signs for the Atkin-Lehner involutions
Class	549b	Isogeny class
Conductor	549	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	73240443 = 39 · 612	Discriminant
Eigenvalues	-1 3+  0 -2  4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-110,-134]	[a1,a2,a3,a4,a6]
Generators	[-8:17:1]	Generators of the group modulo torsion
j	7414875/3721	j-invariant
L	1.3699084866791	L(r)(E,1)/r!
Ω	1.5545806289947	Real period
R	0.88120774254403	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	8784h2 35136f2 549a2 13725a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 549b2

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 549b2

-4	8	-3	5	-7	-11	13	61
8784h2	35136f2	549a2	13725a2	26901h2	66429a2	92781a2	33489c2

---

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