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	19992i	Isogeny class
Conductor	19992	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	5481326592 = 211 · 33 · 73 · 172	Discriminant
Eigenvalues	2+ 3+ -2 7-  0 -6 17-  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8024,-273972]	[a1,a2,a3,a4,a6]
Generators	[842:1525:8]	Generators of the group modulo torsion
j	81344187038/7803	j-invariant
L	3.2486249563952	L(r)(E,1)/r!
Ω	0.50442873009128	Real period
R	6.4402060441866	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	39984y2 59976bh2 19992o2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 19992i2

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	-	0	-6	-	8	-2	-6	8	-4	-10	8	4	-10	14	6	-4	6	-10	-4	6	-6	18

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Quadratic twists for elliptic curve 19992i2

-4	-3	-7
39984y2	59976bh2	19992o2

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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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