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	1022b	Isogeny class
Conductor	1022	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	2181893652512 = 25 · 74 · 734	Discriminant
Eigenvalues	2-  0 -2 7+  0 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-5611,146715]	[a1,a2,a3,a4,a6]
Generators	[79:398:1]	Generators of the group modulo torsion
j	19533135070647297/2181893652512	j-invariant
L	3.0776727915483	L(r)(E,1)/r!
Ω	0.79676263822094	Real period
R	0.38627222762607	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	8176a4 32704a3 9198d4 25550d3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1022b3

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
-	0	-2	+	0	-2	2	0	-8	-6	0	-10	2	-8	8	2	4	2	4	0	-	8	-4	-6	10

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Quadratic twists for elliptic curve 1022b3

-4	8	-3	5	-7	-11	73
8176a4	32704a3	9198d4	25550d3	7154j4	123662l3	74606e3

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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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