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	6840q	Isogeny class
Conductor	6840	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	5263380000000 = 28 · 36 · 57 · 192	Discriminant
Eigenvalues	2- 3- 5+  4 -4 -4  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3749943,2795021242]	[a1,a2,a3,a4,a6]
Generators	[1109:522:1]	Generators of the group modulo torsion
j	31248575021659890256/28203125	j-invariant
L	4.1336061701338	L(r)(E,1)/r!
Ω	0.47887170173426	Real period
R	2.1579925036099	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	13680r2 54720cm2 760b2 34200y2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6840q2

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

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Quadratic twists for elliptic curve 6840q2

-4	8	-3	5	-19
13680r2	54720cm2	760b2	34200y2	129960be2

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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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