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	6840j	Isogeny class
Conductor	6840	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	194940000000000 = 211 · 33 · 510 · 192	Discriminant
Eigenvalues	2- 3+ 5+ -2 -2  0  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-43083,3375782]	[a1,a2,a3,a4,a6]
j	159936580505574/3525390625	j-invariant
L	1.1307828531805	L(r)(E,1)/r!
Ω	0.56539142659026	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13680b2 54720k2 6840b2 34200e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6840j2

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	-2	0	6	+	-8	-6	4	4	-4	-12	0	14	10	10	4	-4	-2	4	-12	0	6

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Quadratic twists for elliptic curve 6840j2

-4	8	-3	5	-19
13680b2	54720k2	6840b2	34200e2	129960e2

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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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