Cremona's table of elliptic curves

21660 = 2² · 3 · 5 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 19+	Signs for the Atkin-Lehner involutions
Class	21660k	Isogeny class
Conductor	21660	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	172368	Modular degree for the optimal curve
Δ	-14857220948266800 = -1 · 24 · 37 · 52 · 198	Discriminant
Eigenvalues	2- 3+ 5-  1 -6  3  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9145,-5871050]	[a1,a2,a3,a4,a6]
Generators	[10710:1108270:1]	Generators of the group modulo torsion
j	-311296/54675	j-invariant
L	4.8043058108685	L(r)(E,1)/r!
Ω	0.17563635458148	Real period
R	4.5589515738513	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	86640dv1 64980k1 108300bm1 21660bd1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 21660k1

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	-6	3	2	+	8	8	-5	1	-6	-5	0	-14	12	-5	3	-14	-13	-1	-16	6	14

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Quadratic twists for elliptic curve 21660k1

-4	-3	5	-19
86640dv1	64980k1	108300bm1	21660bd1

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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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