Cremona's table of elliptic curves

20640 = 2⁵ · 3 · 5 · 43

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 43+	Signs for the Atkin-Lehner involutions
Class	20640k	Isogeny class
Conductor	20640	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2816	Modular degree for the optimal curve
Δ	-8916480 = -1 · 29 · 34 · 5 · 43	Discriminant
Eigenvalues	2+ 3- 5- -1  0 -3  0 -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,40,120]	[a1,a2,a3,a4,a6]
Generators	[-2:6:1]	Generators of the group modulo torsion
j	13481272/17415	j-invariant
L	6.3990320019941	L(r)(E,1)/r!
Ω	1.5559166376868	Real period
R	0.51408859631352	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20640e1 41280cc1 61920bq1 103200bu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20640k1

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
+	-	-	-1	0	-3	0	-3	4	-3	1	4	5	+	-2	2	0	-5	3	-10	-13	7	0	-12	18

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Quadratic twists for elliptic curve 20640k1

-4	8	-3	5
20640e1	41280cc1	61920bq1	103200bu1

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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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