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
deg	1536	Modular degree for the optimal curve
Δ	69290000 = 24 · 54 · 132 · 41	Discriminant
Eigenvalues	2- -2 5+ -2 -2 13+  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-111,-215]	[a1,a2,a3,a4,a6]
Generators	[-4:15:1]	Generators of the group modulo torsion
j	151334226289/69290000	j-invariant
L	3.4883082339624	L(r)(E,1)/r!
Ω	1.5361852266675	Real period
R	0.56769004372113	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	42640f1 47970o1 26650h1 69290j1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5330d1

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 5330d1

-4	-3	5	13
42640f1	47970o1	26650h1	69290j1

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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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