Cremona's table of elliptic curves

4284 = 2² · 3² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 17+	Signs for the Atkin-Lehner involutions
Class	4284g	Isogeny class
Conductor	4284	Conductor
∏ cp	144	Product of Tamagawa factors cp
Δ	-131738935512570624 = -1 · 28 · 37 · 712 · 17	Discriminant
Eigenvalues	2- 3-  3 7-  3 -1 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,119904,-7040252]	[a1,a2,a3,a4,a6]
j	1021544365555712/705905647251	j-invariant
L	2.9753891737511	L(r)(E,1)/r!
Ω	0.18596182335944	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	17136ba2 68544cf2 1428e2 107100bf2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4284g2

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
-	-	3	-	3	-1	+	5	3	6	-10	-4	9	-1	6	-6	6	8	-4	12	-10	-10	-6	-12	8

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Quadratic twists for elliptic curve 4284g2

-4	8	-3	5	-7	17
17136ba2	68544cf2	1428e2	107100bf2	29988bo2	72828r2

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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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