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	6840r	Isogeny class
Conductor	6840	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	378963360000 = 28 · 38 · 54 · 192	Discriminant
Eigenvalues	2- 3- 5+  0  0 -2  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-17103,-860398]	[a1,a2,a3,a4,a6]
j	2964647793616/2030625	j-invariant
L	1.6699725322763	L(r)(E,1)/r!
Ω	0.41749313306908	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	13680g2 54720bm2 2280b2 34200z2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6840r2

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

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Quadratic twists for elliptic curve 6840r2

-4	8	-3	5	-19
13680g2	54720bm2	2280b2	34200z2	129960o2

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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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