Cremona's table of elliptic curves

9842 = 2 · 7 · 19 · 37

Field	Data	Notes
Atkin-Lehner	2- 7+ 19+ 37-	Signs for the Atkin-Lehner involutions
Class	9842g	Isogeny class
Conductor	9842	Conductor
∏ cp	182	Product of Tamagawa factors cp
deg	174720	Modular degree for the optimal curve
Δ	724021883787862016 = 213 · 72 · 19 · 377	Discriminant
Eigenvalues	2- -2 -1 7+  1  4  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-693861,-218721023]	[a1,a2,a3,a4,a6]
Generators	[-444:1591:1]	Generators of the group modulo torsion
j	36943767661565610126289/724021883787862016	j-invariant
L	4.2550082091969	L(r)(E,1)/r!
Ω	0.16561457892563	Real period
R	0.14116611071479	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	78736bb1 88578h1 68894z1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 9842g1

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
-	-2	-1	+	1	4	0	+	1	-6	-4	-	-12	6	12	3	-9	13	-8	3	7	-10	-9	13	2

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Quadratic twists for elliptic curve 9842g1

-4	-3	-7
78736bb1	88578h1	68894z1

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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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