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	9	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	-16014592 = -1 · 28 · 113 · 47	Discriminant
Eigenvalues	2- -2  0 -1 11-  5 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,12,-188]	[a1,a2,a3,a4,a6]
Generators	[16:66:1]	Generators of the group modulo torsion
j	686000/62557	j-invariant
L	2.1788338408151	L(r)(E,1)/r!
Ω	1.0470221571459	Real period
R	2.0809815971368	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	8272j1 33088e1 18612d1 51700i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2068d1

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 2068d1

-4	8	-3	5	-7	-11	-47
8272j1	33088e1	18612d1	51700i1	101332k1	22748d1	97196b1

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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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