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	39840d	Isogeny class
Conductor	39840	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	10752	Modular degree for the optimal curve
Δ	-165336000 = -1 · 26 · 3 · 53 · 832	Discriminant
Eigenvalues	2+ 3+ 5- -2  0  2  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,70,-600]	[a1,a2,a3,a4,a6]
Generators	[15:60:1]	Generators of the group modulo torsion
j	584277056/2583375	j-invariant
L	5.4103662470719	L(r)(E,1)/r!
Ω	0.9165056901684	Real period
R	1.9677514662875	Regulator
r	1	Rank of the group of rational points
S	1.0000000000005	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	39840l1 79680o1 119520q1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 39840d1

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

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Quadratic twists for elliptic curve 39840d1

-4	8	-3
39840l1	79680o1	119520q1

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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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