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	5576b	Isogeny class
Conductor	5576	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	287536744448 = 211 · 174 · 412	Discriminant
Eigenvalues	2+ -2  2  4 -2  0 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3992,92272]	[a1,a2,a3,a4,a6]
Generators	[27:70:1]	Generators of the group modulo torsion
j	3436166063666/140398801	j-invariant
L	3.5045967100281	L(r)(E,1)/r!
Ω	0.96541731848454	Real period
R	3.6301365667745	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	11152b2 44608e2 50184bc2 94792k2	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 5576b2

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

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Quadratic twists for elliptic curve 5576b2

-4	8	-3	17
11152b2	44608e2	50184bc2	94792k2

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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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