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	4284i	Isogeny class
Conductor	4284	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-113328730368 = -1 · 28 · 312 · 72 · 17	Discriminant
Eigenvalues	2- 3- -2 7-  0 -2 17-  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,249,16126]	[a1,a2,a3,a4,a6]
Generators	[-1:126:1]	Generators of the group modulo torsion
j	9148592/607257	j-invariant
L	3.3455603985677	L(r)(E,1)/r!
Ω	0.80298009881961	Real period
R	0.69440500528089	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	17136be2 68544ck2 1428d2 107100q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4284i2

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
-	-	-2	-	0	-2	-	6	-8	4	0	10	-10	-8	8	-6	4	-8	-4	8	4	0	0	-10	0

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Quadratic twists for elliptic curve 4284i2

-4	8	-3	5	-7	17
17136be2	68544ck2	1428d2	107100q2	29988be2	72828n2

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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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