Cremona's table of elliptic curves

1022 = 2 · 7 · 73

Field	Data	Notes
Atkin-Lehner	2- 7+ 73-	Signs for the Atkin-Lehner involutions
Class	1022c	Isogeny class
Conductor	1022	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-32704 = -1 · 26 · 7 · 73	Discriminant
Eigenvalues	2- -2  2 7+ -6 -2 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,8,0]	[a1,a2,a3,a4,a6]
Generators	[2:4:1]	Generators of the group modulo torsion
j	56181887/32704	j-invariant
L	2.7525707289177	L(r)(E,1)/r!
Ω	2.183138244857	Real period
R	0.84055471838982	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	8176c1 32704c1 9198e1 25550e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1022c1

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	-2	-2	-2	0	0	0	-2	-2	-10	0	0	-8	12	-12	-8	-	-8	0	10	-10

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Quadratic twists for elliptic curve 1022c1

-4	8	-3	5	-7	-11	73
8176c1	32704c1	9198e1	25550e1	7154k1	123662r1	74606f1

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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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