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	64	Product of Tamagawa factors cp
Δ	70560000 = 28 · 32 · 54 · 72	Discriminant
Eigenvalues	2- 3+ 5- 7+ -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-180,900]	[a1,a2,a3,a4,a6]
Generators	[-10:40:1]	Generators of the group modulo torsion
j	2533446736/275625	j-invariant
L	2.0729414081239	L(r)(E,1)/r!
Ω	1.887410843796	Real period
R	1.0982989818765	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	1680j2 6720q2 2520e2 4200o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 840f2

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 840f2

-4	8	-3	5	-7	-11
1680j2	6720q2	2520e2	4200o2	5880bf2	101640p2

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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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