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	21780ba	Isogeny class
Conductor	21780	Conductor
∏ cp	120	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	-661567500000000 = -1 · 28 · 37 · 510 · 112	Discriminant
Eigenvalues	2- 3- 5-  3 11- -2 -2  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-39072,-3219964]	[a1,a2,a3,a4,a6]
Generators	[532:11250:1]	Generators of the group modulo torsion
j	-292124360704/29296875	j-invariant
L	6.3556362914782	L(r)(E,1)/r!
Ω	0.16882684831496	Real period
R	0.31371571696647	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	87120gg1 7260c1 108900co1 21780bb1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 21780ba1

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 21780ba1

-4	-3	5	-11
87120gg1	7260c1	108900co1	21780bb1

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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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