Cremona's table of elliptic curves

2822 = 2 · 17 · 83

Field	Data	Notes
Atkin-Lehner	2+ 17- 83+	Signs for the Atkin-Lehner involutions
Class	2822a	Isogeny class
Conductor	2822	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	1520	Modular degree for the optimal curve
Δ	-13048928 = -1 · 25 · 173 · 83	Discriminant
Eigenvalues	2+  1  0 -4 -3 -7 17-  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-706,7156]	[a1,a2,a3,a4,a6]
j	-38837676489625/13048928	j-invariant
L	0.73254837436561	L(r)(E,1)/r!
Ω	2.1976451230968	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	22576g1 90304k1 25398l1 70550z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2822a1

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
+	1	0	-4	-3	-7	-	5	6	9	-10	2	0	11	6	6	0	-1	-4	9	11	8	+	0	2

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Quadratic twists for elliptic curve 2822a1

-4	8	-3	5	17
22576g1	90304k1	25398l1	70550z1	47974c1

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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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