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	6840n	Isogeny class
Conductor	6840	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6720	Modular degree for the optimal curve
Δ	-256010803200 = -1 · 211 · 36 · 52 · 193	Discriminant
Eigenvalues	2- 3- 5+ -1 -4  1  7 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-603,-25002]	[a1,a2,a3,a4,a6]
Generators	[154:1880:1]	Generators of the group modulo torsion
j	-16241202/171475	j-invariant
L	3.6404099297188	L(r)(E,1)/r!
Ω	0.41791061270028	Real period
R	4.3554887326224	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13680o1 54720cf1 760c1 34200r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6840n1

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
-	-	+	-1	-4	1	7	+	5	-7	-2	-6	-6	10	8	3	-5	-8	11	12	-9	6	-14	6	-2

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Quadratic twists for elliptic curve 6840n1

-4	8	-3	5	-19
13680o1	54720cf1	760c1	34200r1	129960s1

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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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