Cremona's table of elliptic curves

21840 = 2⁴ · 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7- 13-	Signs for the Atkin-Lehner involutions
Class	21840ca	Isogeny class
Conductor	21840	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	80928021558558720 = 215 · 3 · 5 · 78 · 134	Discriminant
Eigenvalues	2- 3- 5+ 7- -4 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-145496,16351764]	[a1,a2,a3,a4,a6]
Generators	[390:4368:1]	Generators of the group modulo torsion
j	83161039719198169/19757817763320	j-invariant
L	6.0605498544645	L(r)(E,1)/r!
Ω	0.32186660392894	Real period
R	0.58841824731164	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	2730b4 87360fk3 65520eo3 109200db3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840ca3

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
-	-	+	-	-4	-	6	-4	4	2	4	-10	-2	-4	0	-2	-4	-10	8	-16	6	-16	-4	-10	-2

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Quadratic twists for elliptic curve 21840ca3

-4	8	-3	5
2730b4	87360fk3	65520eo3	109200db3

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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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