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	21780l	Isogeny class
Conductor	21780	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	380160	Modular degree for the optimal curve
Δ	-3267368501897491200 = -1 · 28 · 39 · 52 · 1110	Discriminant
Eigenvalues	2- 3- 5+  3 11-  6  2  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-702768,-242864908]	[a1,a2,a3,a4,a6]
j	-7929856/675	j-invariant
L	2.6254826578886	L(r)(E,1)/r!
Ω	0.08204633305902	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	87120eu1 7260i1 108900cq1 21780m1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 21780l1

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	-	6	2	1	-6	-4	-3	-3	2	8	-4	-2	-8	5	-1	2	13	-1	12	6	-9

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Quadratic twists for elliptic curve 21780l1

-4	-3	5	-11
87120eu1	7260i1	108900cq1	21780m1

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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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