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	8	Product of Tamagawa factors cp
Δ	15701948 = 22 · 174 · 47	Discriminant
Eigenvalues	2-  0  2 -4 -4 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1009,12581]	[a1,a2,a3,a4,a6]
Generators	[694:5701:8]	Generators of the group modulo torsion
j	113499416527713/15701948	j-invariant
L	3.8845817208985	L(r)(E,1)/r!
Ω	2.1294151100364	Real period
R	3.6484964369697	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	12784e3 51136c4 14382d3 39950c4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1598b4

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 1598b4

-4	8	-3	5	-7	17	-47
12784e3	51136c4	14382d3	39950c4	78302e4	27166b4	75106e4

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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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