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	20640t	Isogeny class
Conductor	20640	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	10240	Modular degree for the optimal curve
Δ	5990760000 = 26 · 34 · 54 · 432	Discriminant
Eigenvalues	2- 3- 5+  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-466,920]	[a1,a2,a3,a4,a6]
Generators	[26:84:1]	Generators of the group modulo torsion
j	175239948736/93605625	j-invariant
L	5.5506992353858	L(r)(E,1)/r!
Ω	1.1772637431052	Real period
R	2.3574578202609	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	20640a1 41280s2 61920q1 103200f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20640t1

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	-4	-2	2	4	4	-6	4	2	-6	+	-4	6	4	10	-12	0	-14	-4	12	18	2

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Quadratic twists for elliptic curve 20640t1

-4	8	-3	5
20640a1	41280s2	61920q1	103200f1

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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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