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	21780u	Isogeny class
Conductor	21780	Conductor
∏ cp	27	Product of Tamagawa factors cp
Δ	-5000563975968000 = -1 · 28 · 36 · 53 · 118	Discriminant
Eigenvalues	2- 3- 5- -1 11-  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-475167,126117574]	[a1,a2,a3,a4,a6]
Generators	[-57:12370:1]	Generators of the group modulo torsion
j	-296587984/125	j-invariant
L	5.6472419988862	L(r)(E,1)/r!
Ω	0.42483362363549	Real period
R	4.4309440093749	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	87120fo2 2420d2 108900bs2 21780t2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 21780u2

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	-	2	0	2	0	6	-4	-4	-9	-1	3	6	0	-1	-13	12	-16	-10	-12	3	-10

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Quadratic twists for elliptic curve 21780u2

-4	-3	5	-11
87120fo2	2420d2	108900bs2	21780t2

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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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