Cremona's table of elliptic curves

2068 = 2² · 11 · 47

Field	Data	Notes
Atkin-Lehner	2- 11+ 47-	Signs for the Atkin-Lehner involutions
Class	2068b	Isogeny class
Conductor	2068	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-91074984704 = -1 · 28 · 115 · 472	Discriminant
Eigenvalues	2-  1 -1  4 11+ -2 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,619,13463]	[a1,a2,a3,a4,a6]
Generators	[-7:94:1]	Generators of the group modulo torsion
j	102294880256/355761659	j-invariant
L	3.4883426416797	L(r)(E,1)/r!
Ω	0.76036393549931	Real period
R	0.76462127296736	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8272o1 33088o1 18612i1 51700d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2068b1

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	-1	4	+	-2	-6	-6	-5	0	-5	7	4	0	-	2	3	0	-7	-5	8	8	0	-9	-3

---

Quadratic twists for elliptic curve 2068b1

-4	8	-3	5	-7	-11	-47
8272o1	33088o1	18612i1	51700d1	101332d1	22748f1	97196d1

---

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