Cremona's table of elliptic curves

39840 = 2⁵ · 3 · 5 · 83

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 83-	Signs for the Atkin-Lehner involutions
Class	39840h	Isogeny class
Conductor	39840	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-2571305472000 = -1 · 212 · 36 · 53 · 832	Discriminant
Eigenvalues	2- 3+ 5+  0  2  0 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2321,89121]	[a1,a2,a3,a4,a6]
Generators	[-7:324:1]	Generators of the group modulo torsion
j	-337735169344/627760125	j-invariant
L	4.0992418819078	L(r)(E,1)/r!
Ω	0.72443167825819	Real period
R	1.414640608955	Regulator
r	1	Rank of the group of rational points
S	0.99999999999953	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	39840e2 79680x1 119520j2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 39840h2

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
-	+	+	0	2	0	-4	-6	0	-2	4	-2	6	8	-8	-6	6	10	-4	0	0	-2	-	10	-8

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Quadratic twists for elliptic curve 39840h2

-4	8	-3
39840e2	79680x1	119520j2

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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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