Cremona's table of elliptic curves

5082 = 2 · 3 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	5082r	Isogeny class
Conductor	5082	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1089371833242 = 2 · 3 · 7 · 1110	Discriminant
Eigenvalues	2- 3+ -2 7+ 11- -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-27409,1734437]	[a1,a2,a3,a4,a6]
Generators	[782:-117:8]	Generators of the group modulo torsion
j	1285429208617/614922	j-invariant
L	4.1902654906966	L(r)(E,1)/r!
Ω	0.85940246292775	Real period
R	4.8757894833365	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	40656dj4 15246l3 127050dk4 35574dd4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082r4

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	+	-	-2	6	4	-4	-2	-4	-2	6	0	-8	-14	12	14	4	12	-6	0	0	-6	-14

---

Quadratic twists for elliptic curve 5082r4

-4	-3	5	-7	-11
40656dj4	15246l3	127050dk4	35574dd4	462c3

---

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