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	6840u	Isogeny class
Conductor	6840	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	1884413258496000 = 211 · 318 · 53 · 19	Discriminant
Eigenvalues	2- 3- 5-  0  4 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-914187,336428134]	[a1,a2,a3,a4,a6]
Generators	[558:230:1]	Generators of the group modulo torsion
j	56594125707224978/1262172375	j-invariant
L	4.5462401841545	L(r)(E,1)/r!
Ω	0.43294430936434	Real period
R	3.5002501752319	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	13680t3 54720o4 2280c3 34200ba4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6840u4

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	2	-	-8	-6	-8	-10	2	-8	8	6	8	-10	4	-16	-6	-16	-4	-6	14

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Quadratic twists for elliptic curve 6840u4

-4	8	-3	5	-19
13680t3	54720o4	2280c3	34200ba4	129960bi4

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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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