Cremona's table of elliptic curves

21960 = 2³ · 3² · 5 · 61

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 61+	Signs for the Atkin-Lehner involutions
Class	21960s	Isogeny class
Conductor	21960	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	473088	Modular degree for the optimal curve
Δ	4.6947941136461E+19	Discriminant
Eigenvalues	2- 3- 5+  2 -4 -2  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-915318,-70235883]	[a1,a2,a3,a4,a6]
Generators	[867190782:43854478011:300763]	Generators of the group modulo torsion
j	7270967611425540096/4025029246953125	j-invariant
L	4.9853703799267	L(r)(E,1)/r!
Ω	0.16533135899634	Real period
R	15.076904980976	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	43920h1 2440b1 109800o1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 21960s1

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	-4	-2	4	4	2	-10	4	0	-6	10	8	-12	4	+	-10	0	6	-12	-8	-6	10

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Quadratic twists for elliptic curve 21960s1

-4	-3	5
43920h1	2440b1	109800o1

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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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