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	4	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	2241000000 = 26 · 33 · 56 · 83	Discriminant
Eigenvalues	2- 3+ 5+  0  2  0 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2946,62496]	[a1,a2,a3,a4,a6]
Generators	[40:84:1]	Generators of the group modulo torsion
j	44196652398016/35015625	j-invariant
L	4.0992418819078	L(r)(E,1)/r!
Ω	1.4488633565164	Real period
R	2.8292812179099	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	39840e1 79680x2 119520j1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 39840h1

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 39840h1

-4	8	-3
39840e1	79680x2	119520j1

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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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