Cremona's table of elliptic curves

840 = 2³ · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7+	Signs for the Atkin-Lehner involutions
Class	840f	Isogeny class
Conductor	840	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3292047360 = 211 · 38 · 5 · 72	Discriminant
Eigenvalues	2- 3+ 5- 7+ -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-10480,-409460]	[a1,a2,a3,a4,a6]
Generators	[986:3159:8]	Generators of the group modulo torsion
j	62161150998242/1607445	j-invariant
L	2.0729414081239	L(r)(E,1)/r!
Ω	0.471852710949	Real period
R	4.3931959275061	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	1680j5 6720q5 2520e5 4200o5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 840f5

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	-2	2	-4	0	-10	0	6	-6	-4	-8	6	-4	-10	4	-16	-14	8	-4	10	10

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Quadratic twists for elliptic curve 840f5

-4	8	-3	5	-7	-11
1680j5	6720q5	2520e5	4200o5	5880bf5	101640p6

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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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