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	12	Product of Tamagawa factors cp
Δ	2088968 = 23 · 72 · 732	Discriminant
Eigenvalues	2- -2  2 7+ -6 -2 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-32,-8]	[a1,a2,a3,a4,a6]
Generators	[-2:8:1]	Generators of the group modulo torsion
j	3630961153/2088968	j-invariant
L	2.7525707289177	L(r)(E,1)/r!
Ω	2.183138244857	Real period
R	0.42027735919491	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	8176c2 32704c2 9198e2 25550e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1022c2

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 1022c2

-4	8	-3	5	-7	-11	73
8176c2	32704c2	9198e2	25550e2	7154k2	123662r2	74606f2

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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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