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	2068d	Isogeny class
Conductor	2068	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-292365568 = -1 · 28 · 11 · 473	Discriminant
Eigenvalues	2- -2  0 -1 11-  5 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2188,-40140]	[a1,a2,a3,a4,a6]
Generators	[810:7095:8]	Generators of the group modulo torsion
j	-4527142594000/1142053	j-invariant
L	2.1788338408151	L(r)(E,1)/r!
Ω	0.34900738571529	Real period
R	6.2429447914104	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	8272j2 33088e2 18612d2 51700i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2068d2

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	0	-1	-	5	-6	-4	9	-6	5	-1	9	8	+	-9	-12	2	-7	6	-10	5	3	-15	-7

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Quadratic twists for elliptic curve 2068d2

-4	8	-3	5	-7	-11	-47
8272j2	33088e2	18612d2	51700i2	101332k2	22748d2	97196b2

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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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