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	6840f	Isogeny class
Conductor	6840	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-1459261578240 = -1 · 210 · 37 · 5 · 194	Discriminant
Eigenvalues	2+ 3- 5+  4  0  2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1797,50182]	[a1,a2,a3,a4,a6]
j	859687196/1954815	j-invariant
L	2.3671340820931	L(r)(E,1)/r!
Ω	0.59178352052326	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	13680q4 54720cj3 2280j4 34200ck3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6840f4

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

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Quadratic twists for elliptic curve 6840f4

-4	8	-3	5	-19
13680q4	54720cj3	2280j4	34200ck3	129960cn3

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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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