Cremona's table of elliptic curves

6840 = 2³ · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 19+	Signs for the Atkin-Lehner involutions
Class	6840m	Isogeny class
Conductor	6840	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2918523156480 = 211 · 37 · 5 · 194	Discriminant
Eigenvalues	2- 3- 5+  0 -4  2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6843,201782]	[a1,a2,a3,a4,a6]
Generators	[626:3051:8]	Generators of the group modulo torsion
j	23735908082/1954815	j-invariant
L	3.6713513043986	L(r)(E,1)/r!
Ω	0.78434623804452	Real period
R	4.6807788784093	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	13680l3 54720cc3 2280a3 34200q3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6840m4

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
-	-	+	0	-4	2	-6	+	4	10	4	10	-6	0	12	-10	0	-10	4	0	10	4	-12	-14	-2

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Quadratic twists for elliptic curve 6840m4

-4	8	-3	5	-19
13680l3	54720cc3	2280a3	34200q3	129960r3

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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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