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	5330c	Isogeny class
Conductor	5330	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	27971840 = 28 · 5 · 13 · 412	Discriminant
Eigenvalues	2-  2 5+  0 -2 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2271,40709]	[a1,a2,a3,a4,a6]
Generators	[-9:250:1]	Generators of the group modulo torsion
j	1295349813487729/27971840	j-invariant
L	7.0279005981042	L(r)(E,1)/r!
Ω	1.9428092268042	Real period
R	0.90434774824295	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	42640h1 47970n1 26650i1 69290h1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5330c1

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

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Quadratic twists for elliptic curve 5330c1

-4	-3	5	13
42640h1	47970n1	26650i1	69290h1

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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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