Cremona's table of elliptic curves

98192 = 2⁴ · 17 · 19²

Field	Data	Notes
Atkin-Lehner	2- 17+ 19-	Signs for the Atkin-Lehner involutions
Class	98192o	Isogeny class
Conductor	98192	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1140480	Modular degree for the optimal curve
Δ	-1124247514548992 = -1 · 28 · 173 · 197	Discriminant
Eigenvalues	2- -1  2  0 -2 -2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5789477,5363687353]	[a1,a2,a3,a4,a6]
Generators	[2141:52706:1]	Generators of the group modulo torsion
j	-1781887227854848/93347	j-invariant
L	5.0056475545961	L(r)(E,1)/r!
Ω	0.36669213429406	Real period
R	3.4127044706346	Regulator
r	1	Rank of the group of rational points
S	1.0000000020754	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24548a1 5168f1	Quadratic twists by: -4 -19

Hecke Eigenvalues for elliptic curve 98192o1

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	2	0	-2	-2	+	-	-8	-1	7	2	2	-1	1	-2	6	14	6	8	-6	8	-3	-6	5

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Quadratic twists for elliptic curve 98192o1

-4	-19
24548a1	5168f1

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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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