Cremona's table of elliptic curves

4556 = 2² · 17 · 67

Field	Data	Notes
Atkin-Lehner	2- 17- 67+	Signs for the Atkin-Lehner involutions
Class	4556b	Isogeny class
Conductor	4556	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	20520	Modular degree for the optimal curve
Δ	-2034019257676544 = -1 · 28 · 179 · 67	Discriminant
Eigenvalues	2- -1  2 -4  5  0 17- -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1717,2170625]	[a1,a2,a3,a4,a6]
Generators	[-56:1445:1]	Generators of the group modulo torsion
j	-2188001148928/7945387725299	j-invariant
L	3.1864162707527	L(r)(E,1)/r!
Ω	0.37358527341468	Real period
R	0.94769863134531	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	18224k1 72896h1 41004c1 113900b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4556b1

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
-	-1	2	-4	5	0	-	-5	0	8	-1	10	-7	-8	0	-6	-5	-1	+	-2	12	-11	3	9	-2

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Quadratic twists for elliptic curve 4556b1

-4	8	-3	5	17
18224k1	72896h1	41004c1	113900b1	77452a1

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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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