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	267387904 = 210 · 72 · 732	Discriminant
Eigenvalues	2-  0 -2 7+  0 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-5451,156251]	[a1,a2,a3,a4,a6]
Generators	[27:154:1]	Generators of the group modulo torsion
j	17909256772123137/267387904	j-invariant
L	3.0776727915483	L(r)(E,1)/r!
Ω	1.5935252764419	Real period
R	0.77254445525214	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8176a2 32704a2 9198d2 25550d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1022b2

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 1022b2

-4	8	-3	5	-7	-11	73
8176a2	32704a2	9198d2	25550d2	7154j2	123662l2	74606e2

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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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