Cremona's table of elliptic curves

5586 = 2 · 3 · 7² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 19-	Signs for the Atkin-Lehner involutions
Class	5586j	Isogeny class
Conductor	5586	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	491545880255556 = 22 · 310 · 78 · 192	Discriminant
Eigenvalues	2+ 3+  2 7- -4  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-55934,-5002080]	[a1,a2,a3,a4,a6]
Generators	[447:7494:1]	Generators of the group modulo torsion
j	164503536215257/4178071044	j-invariant
L	2.7503315533901	L(r)(E,1)/r!
Ω	0.31092260177424	Real period
R	4.42285562017	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	44688cw2 16758bp2 798d2 106134da2	Quadratic twists by: -4 -3 -7 -19

Hecke Eigenvalues for elliptic curve 5586j2

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
+	+	2	-	-4	2	2	-	-4	2	-4	-6	10	-4	8	10	-12	2	-8	-16	-10	-8	0	10	2

---

Quadratic twists for elliptic curve 5586j2

-4	-3	-7	-19
44688cw2	16758bp2	798d2	106134da2

---

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