Cremona's table of elliptic curves

5555 = 5 · 11 · 101

Field	Data	Notes
Atkin-Lehner	5+ 11- 101-	Signs for the Atkin-Lehner involutions
Class	5555a	Isogeny class
Conductor	5555	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	154290125 = 53 · 112 · 1012	Discriminant
Eigenvalues	1 -2 5+ -4 11-  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-644,6201]	[a1,a2,a3,a4,a6]
Generators	[11:16:1]	Generators of the group modulo torsion
j	29472131485369/154290125	j-invariant
L	2.3645486951623	L(r)(E,1)/r!
Ω	1.8344851562946	Real period
R	1.2889440326344	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	88880h2 49995g2 27775d2 61105a2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 5555a2

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	-	4	0	-4	0	-2	8	-6	6	10	12	-12	-8	-10	-2	0	10	-4	0	14	-2

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Quadratic twists for elliptic curve 5555a2

-4	-3	5	-11
88880h2	49995g2	27775d2	61105a2

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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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