Cremona's table of elliptic curves

19992 = 2³ · 3 · 7² · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 17+	Signs for the Atkin-Lehner involutions
Class	19992v	Isogeny class
Conductor	19992	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-181115820361728 = -1 · 211 · 32 · 76 · 174	Discriminant
Eigenvalues	2- 3+ -2 7-  4 -6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,14096,-70580]	[a1,a2,a3,a4,a6]
Generators	[21:484:1]	Generators of the group modulo torsion
j	1285471294/751689	j-invariant
L	3.2527851808857	L(r)(E,1)/r!
Ω	0.33549838118773	Real period
R	4.8476913202535	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	39984r3 59976r3 408b4	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 19992v4

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	-	4	-6	+	-4	-4	-6	4	10	6	4	8	6	4	14	-12	-12	-10	-4	-4	6	6

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Quadratic twists for elliptic curve 19992v4

-4	-3	-7
39984r3	59976r3	408b4

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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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