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	21780bb	Isogeny class
Conductor	21780	Conductor
∏ cp	120	Product of Tamagawa factors cp
deg	887040	Modular degree for the optimal curve
Δ	-1.1720071818675E+21	Discriminant
Eigenvalues	2- 3- 5- -3 11-  2  2 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4727712,4285772084]	[a1,a2,a3,a4,a6]
Generators	[1573:27225:1]	Generators of the group modulo torsion
j	-292124360704/29296875	j-invariant
L	5.1115194670652	L(r)(E,1)/r!
Ω	0.15032676711581	Real period
R	0.28335602751346	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	87120ge1 7260d1 108900ck1 21780ba1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 21780bb1

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
-	-	-	-3	-	2	2	-1	2	-8	5	-11	6	8	-8	-2	-4	3	-9	6	11	9	8	-6	7

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Quadratic twists for elliptic curve 21780bb1

-4	-3	5	-11
87120ge1	7260d1	108900ck1	21780ba1

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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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