Cremona's table of elliptic curves

1598 = 2 · 17 · 47

Field	Data	Notes
Atkin-Lehner	2- 17- 47+	Signs for the Atkin-Lehner involutions
Class	1598b	Isogeny class
Conductor	1598	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	331818308 = 22 · 17 · 474	Discriminant
Eigenvalues	2-  0  2 -4 -4 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-409,-2955]	[a1,a2,a3,a4,a6]
Generators	[43:218:1]	Generators of the group modulo torsion
j	7549145158113/331818308	j-invariant
L	3.8845817208985	L(r)(E,1)/r!
Ω	1.0647075550182	Real period
R	3.6484964369697	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	12784e4 51136c3 14382d4 39950c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1598b3

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

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Quadratic twists for elliptic curve 1598b3

-4	8	-3	5	-7	17	-47
12784e4	51136c3	14382d4	39950c3	78302e3	27166b3	75106e3

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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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