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	840g	Isogeny class
Conductor	840	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	205752960000 = 210 · 38 · 54 · 72	Discriminant
Eigenvalues	2- 3+ 5- 7-  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1720,-16100]	[a1,a2,a3,a4,a6]
j	549871953124/200930625	j-invariant
L	1.527981036942	L(r)(E,1)/r!
Ω	0.76399051847101	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1680h3 6720w3 2520g3 4200k3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 840g3

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	-6	4	8	-2	0	-2	10	4	0	14	12	-2	-4	0	2	-8	-4	-6	-6

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Quadratic twists for elliptic curve 840g3

-4	8	-3	5	-7	-11
1680h3	6720w3	2520g3	4200k3	5880bc3	101640k4

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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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