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	5576j	Isogeny class
Conductor	5576	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	7315712 = 28 · 17 · 412	Discriminant
Eigenvalues	2- -2 -2 -2  2 -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9524,354592]	[a1,a2,a3,a4,a6]
Generators	[-42:826:1] [-8:656:1]	Generators of the group modulo torsion
j	373239420296272/28577	j-invariant
L	3.3883588389294	L(r)(E,1)/r!
Ω	1.7915721366275	Real period
R	0.94563840597275	Regulator
r	2	Rank of the group of rational points
S	0.99999999999948	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11152j1 44608v1 50184g1 94792t1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 5576j1

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

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Quadratic twists for elliptic curve 5576j1

-4	8	-3	17
11152j1	44608v1	50184g1	94792t1

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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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