Cremona's table of elliptic curves

5166 = 2 · 3² · 7 · 41

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 41-	Signs for the Atkin-Lehner involutions
Class	5166r	Isogeny class
Conductor	5166	Conductor
∏ cp	7	Product of Tamagawa factors cp
Δ	7950648476917944 = 23 · 36 · 7 · 417	Discriminant
Eigenvalues	2+ 3-  1 7-  2  0  3 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-86501814,309682215836]	[a1,a2,a3,a4,a6]
j	98191033604529537629349729/10906239337336	j-invariant
L	1.6451075931457	L(r)(E,1)/r!
Ω	0.23501537044939	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41328bi2 574i2 129150cr2 36162r2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5166r2

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	-	2	0	3	-8	4	5	-3	10	-	-5	-6	9	10	13	-2	-9	4	-11	14	1	7

---

Quadratic twists for elliptic curve 5166r2

-4	-3	5	-7
41328bi2	574i2	129150cr2	36162r2

---

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