Cremona's table of elliptic curves

21780 = 2² · 3² · 5 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 11-	Signs for the Atkin-Lehner involutions
Class	21780y	Isogeny class
Conductor	21780	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	2582935938000 = 24 · 36 · 53 · 116	Discriminant
Eigenvalues	2- 3- 5- -2 11- -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-45012,-3674891]	[a1,a2,a3,a4,a6]
Generators	[275:2178:1]	Generators of the group modulo torsion
j	488095744/125	j-invariant
L	4.8942834696182	L(r)(E,1)/r!
Ω	0.32777373616786	Real period
R	2.4886493992469	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	87120fz3 2420e3 108900bx3 180a3	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 21780y3

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	-	-2	-6	4	-6	6	-4	2	6	10	6	6	-12	-2	2	12	-2	-8	6	6	2

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Quadratic twists for elliptic curve 21780y3

-4	-3	5	-11
87120fz3	2420e3	108900bx3	180a3

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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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