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	1022a	Isogeny class
Conductor	1022	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	400	Modular degree for the optimal curve
Δ	3662848 = 210 · 72 · 73	Discriminant
Eigenvalues	2+  0  4 7+  6 -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-85,-267]	[a1,a2,a3,a4,a6]
j	68367756969/3662848	j-invariant
L	1.5767090425424	L(r)(E,1)/r!
Ω	1.5767090425424	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8176b1 32704b1 9198j1 25550r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1022a1

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	4	+	6	-4	6	-4	8	0	-4	2	10	-6	0	-4	-10	2	12	-8	-	-8	14	6	-2

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Quadratic twists for elliptic curve 1022a1

-4	8	-3	5	-7	-11	73
8176b1	32704b1	9198j1	25550r1	7154e1	123662bd1	74606c1

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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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