Cremona's table of elliptic curves

5576 = 2³ · 17 · 41

Field	Data	Notes
Atkin-Lehner	2- 17+ 41-	Signs for the Atkin-Lehner involutions
Class	5576h	Isogeny class
Conductor	5576	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	18746512 = 24 · 17 · 413	Discriminant
Eigenvalues	2- -1  0 -3 -4  6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-288,1969]	[a1,a2,a3,a4,a6]
Generators	[1:41:1]	Generators of the group modulo torsion
j	165686944000/1171657	j-invariant
L	2.7809747295119	L(r)(E,1)/r!
Ω	2.1867621049437	Real period
R	0.21195528640456	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	11152c1 44608i1 50184k1 94792q1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 5576h1

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	0	-3	-4	6	+	4	4	9	-8	2	-	5	-8	-2	9	12	2	-9	8	-1	-5	10	-18

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Quadratic twists for elliptic curve 5576h1

-4	8	-3	17
11152c1	44608i1	50184k1	94792q1

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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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