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
Δ	7797600000000 = 211 · 33 · 58 · 192	Discriminant
Eigenvalues	2+ 3+ 5+  0 -2  0  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12003,487998]	[a1,a2,a3,a4,a6]
Generators	[102:570:1]	Generators of the group modulo torsion
j	3458592648054/141015625	j-invariant
L	3.763702617625	L(r)(E,1)/r!
Ω	0.73331629846852	Real period
R	2.5662204873158	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	13680a2 54720j2 6840l2 34200bs2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6840a2

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 6840a2

-4	8	-3	5	-19
13680a2	54720j2	6840l2	34200bs2	129960bm2

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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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