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	4284c	Isogeny class
Conductor	4284	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	4197360384 = 28 · 39 · 72 · 17	Discriminant
Eigenvalues	2- 3+ -2 7-  2  2 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2511,-48330]	[a1,a2,a3,a4,a6]
Generators	[-29:10:1]	Generators of the group modulo torsion
j	347482224/833	j-invariant
L	3.421769727648	L(r)(E,1)/r!
Ω	0.67452870817077	Real period
R	1.6909434623014	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	17136n2 68544p2 4284d2 107100c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4284c2

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	-	2	2	+	-6	-6	6	4	2	-6	12	-8	-4	-12	0	4	-2	-16	0	4	10	12

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Quadratic twists for elliptic curve 4284c2

-4	8	-3	5	-7	17
17136n2	68544p2	4284d2	107100c2	29988n2	72828a2

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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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