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	6840a	Isogeny class
Conductor	6840	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	328320000 = 210 · 33 · 54 · 19	Discriminant
Eigenvalues	2+ 3+ 5+  0 -2  0  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-11883,498582]	[a1,a2,a3,a4,a6]
Generators	[31:400:1]	Generators of the group modulo torsion
j	6711788809548/11875	j-invariant
L	3.763702617625	L(r)(E,1)/r!
Ω	1.466632596937	Real period
R	1.2831102436579	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	13680a1 54720j1 6840l1 34200bs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6840a1

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

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Quadratic twists for elliptic curve 6840a1

-4	8	-3	5	-19
13680a1	54720j1	6840l1	34200bs1	129960bm1

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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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