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	5576d	Isogeny class
Conductor	5576	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	608	Modular degree for the optimal curve
Δ	11152 = 24 · 17 · 41	Discriminant
Eigenvalues	2+  1 -2  3  4 -2 17- -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-124,-575]	[a1,a2,a3,a4,a6]
Generators	[-54:1:8]	Generators of the group modulo torsion
j	13285149952/697	j-invariant
L	4.4094452699558	L(r)(E,1)/r!
Ω	1.42972999174	Real period
R	1.5420552465958	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	11152h1 44608t1 50184v1 94792d1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 5576d1

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	3	4	-2	-	-6	2	-5	-6	10	-	5	-2	-12	-7	0	-2	-7	2	-11	11	4	-2

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Quadratic twists for elliptic curve 5576d1

-4	8	-3	17
11152h1	44608t1	50184v1	94792d1

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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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