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	5330f	Isogeny class
Conductor	5330	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	896	Modular degree for the optimal curve
Δ	-213200 = -1 · 24 · 52 · 13 · 41	Discriminant
Eigenvalues	2- -3 5-  0  2 13+ -4  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,3,21]	[a1,a2,a3,a4,a6]
Generators	[1:4:1]	Generators of the group modulo torsion
j	4019679/213200	j-invariant
L	3.833003155102	L(r)(E,1)/r!
Ω	2.4012367662873	Real period
R	0.19953275791648	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	42640o1 47970g1 26650d1 69290e1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5330f1

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
-	-3	-	0	2	+	-4	2	-4	-6	1	-2	+	-4	-6	0	11	11	-8	6	-4	0	5	3	-1

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Quadratic twists for elliptic curve 5330f1

-4	-3	5	13
42640o1	47970g1	26650d1	69290e1

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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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