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	20640j	Isogeny class
Conductor	20640	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	19410062400 = 26 · 38 · 52 · 432	Discriminant
Eigenvalues	2+ 3- 5-  0  4 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2330,42000]	[a1,a2,a3,a4,a6]
Generators	[-2:216:1]	Generators of the group modulo torsion
j	21867436817344/303282225	j-invariant
L	6.9361395662532	L(r)(E,1)/r!
Ω	1.2231907861242	Real period
R	1.4176324014488	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	20640s1 41280j2 61920bp1 103200bs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20640j1

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	-6	2	0	0	-2	4	-10	-6	+	0	-6	4	-2	-12	-16	14	4	4	2	10

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Quadratic twists for elliptic curve 20640j1

-4	8	-3	5
20640s1	41280j2	61920bp1	103200bs1

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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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