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	21660p	Isogeny class
Conductor	21660	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	12960	Modular degree for the optimal curve
Δ	2599200000 = 28 · 32 · 55 · 192	Discriminant
Eigenvalues	2- 3+ 5- -2 -1 -4 -8 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-405,2097]	[a1,a2,a3,a4,a6]
Generators	[-21:30:1] [-8:69:1]	Generators of the group modulo torsion
j	79691776/28125	j-invariant
L	6.612049212255	L(r)(E,1)/r!
Ω	1.3232456715185	Real period
R	0.16656139154844	Regulator
r	2	Rank of the group of rational points
S	0.9999999999997	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	86640eb1 64980u1 108300cc1 21660ba1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 21660p1

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
-	+	-	-2	-1	-4	-8	-	-2	-3	-7	-8	-10	-12	-6	6	3	5	-14	-1	-4	-3	16	-15	18

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Quadratic twists for elliptic curve 21660p1

-4	-3	5	-19
86640eb1	64980u1	108300cc1	21660ba1

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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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