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	20640a	Isogeny class
Conductor	20640	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	77400000000 = 29 · 32 · 58 · 43	Discriminant
Eigenvalues	2+ 3+ 5+  0  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4336,110536]	[a1,a2,a3,a4,a6]
j	17612529277832/151171875	j-invariant
L	1.0922844050688	L(r)(E,1)/r!
Ω	1.0922844050688	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20640t2 41280bj4 61920ca3 103200ch3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20640a3

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 20640a3

-4	8	-3	5
20640t2	41280bj4	61920ca3	103200ch3

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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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