Cremona's table of elliptic curves

39984 = 2⁴ · 3 · 7² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 17-	Signs for the Atkin-Lehner involutions
Class	39984i	Isogeny class
Conductor	39984	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	422603580844032 = 211 · 3 · 77 · 174	Discriminant
Eigenvalues	2+ 3+ -2 7-  4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-48624,4022880]	[a1,a2,a3,a4,a6]
Generators	[341:5194:1]	Generators of the group modulo torsion
j	52767497666/1753941	j-invariant
L	4.1015592733451	L(r)(E,1)/r!
Ω	0.52742351894285	Real period
R	3.8882976640539	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	19992ba3 119952x3 5712j3	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 39984i3

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	-2	-	-4	4	-2	0	2	10	4	-8	6	-8	-2	4	-12	10	-8	0	-6	-6

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Quadratic twists for elliptic curve 39984i3

-4	-3	-7
19992ba3	119952x3	5712j3

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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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