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
deg	192	Modular degree for the optimal curve
Δ	-204544 = -1 · 28 · 17 · 47	Discriminant
Eigenvalues	2-  0  2 -4 -4 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,11,13]	[a1,a2,a3,a4,a6]
Generators	[1:4:1]	Generators of the group modulo torsion
j	160103007/204544	j-invariant
L	3.8845817208985	L(r)(E,1)/r!
Ω	2.1294151100364	Real period
R	0.91212410924242	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	12784e1 51136c1 14382d1 39950c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1598b1

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 1598b1

-4	8	-3	5	-7	17	-47
12784e1	51136c1	14382d1	39950c1	78302e1	27166b1	75106e1

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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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