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	2068a	Isogeny class
Conductor	2068	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-13741181696 = -1 · 28 · 11 · 474	Discriminant
Eigenvalues	2-  1  1 -2 11+  0 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,595,1007]	[a1,a2,a3,a4,a6]
Generators	[2:47:1]	Generators of the group modulo torsion
j	90845732864/53676491	j-invariant
L	3.4492818474928	L(r)(E,1)/r!
Ω	0.76407442548171	Real period
R	0.37619392086905	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	8272n1 33088p1 18612j1 51700b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2068a1

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	-2	+	0	-2	-4	9	0	-7	7	-8	-6	-	-14	3	4	-5	7	-12	-10	2	-9	17

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Quadratic twists for elliptic curve 2068a1

-4	8	-3	5	-7	-11	-47
8272n1	33088p1	18612j1	51700b1	101332e1	22748e1	97196e1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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