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	-531284060160 = -1 · 211 · 32 · 5 · 78	Discriminant
Eigenvalues	2- 3+ 5- 7+ -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1120,-32340]	[a1,a2,a3,a4,a6]
Generators	[57:462:1]	Generators of the group modulo torsion
j	75798394558/259416045	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	1680j6 6720q6 2520e6 4200o6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 840f6

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 840f6

-4	8	-3	5	-7	-11
1680j6	6720q6	2520e6	4200o6	5880bf6	101640p5

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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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