Cremona's table of elliptic curves

5330 = 2 · 5 · 13 · 41

Field	Data	Notes
Atkin-Lehner	2- 5+ 13+ 41-	Signs for the Atkin-Lehner involutions
Class	5330d	Isogeny class
Conductor	5330	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-4801104100 = -1 · 22 · 52 · 134 · 412	Discriminant
Eigenvalues	2- -2 5+ -2 -2 13+  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,389,-1515]	[a1,a2,a3,a4,a6]
Generators	[14:75:1]	Generators of the group modulo torsion
j	6508827125711/4801104100	j-invariant
L	3.4883082339624	L(r)(E,1)/r!
Ω	0.76809261333373	Real period
R	1.1353800874423	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	42640f2 47970o2 26650h2 69290j2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5330d2

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	+	6	2	0	-2	4	-6	-	8	-6	10	0	-2	-2	2	-10	14	-16	-6	-2

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Quadratic twists for elliptic curve 5330d2

-4	-3	5	13
42640f2	47970o2	26650h2	69290j2

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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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