Cremona's table of elliptic curves

2132 = 2² · 13 · 41

Field	Data	Notes
Atkin-Lehner	2- 13+ 41-	Signs for the Atkin-Lehner involutions
Class	2132b	Isogeny class
Conductor	2132	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	8528 = 24 · 13 · 41	Discriminant
Eigenvalues	2- -2  2  4  0 13+ -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-177,-968]	[a1,a2,a3,a4,a6]
Generators	[17:35:1]	Generators of the group modulo torsion
j	38545604608/533	j-invariant
L	2.7058387996085	L(r)(E,1)/r!
Ω	1.3082848751099	Real period
R	2.7576448637317	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	8528h1 34112k1 19188k1 53300g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2132b1

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	4	0	+	-6	-8	0	-6	-10	2	-	8	0	2	-14	-10	8	8	-14	-2	14	-6	-18

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Quadratic twists for elliptic curve 2132b1

-4	8	-3	5	-7	13	41
8528h1	34112k1	19188k1	53300g1	104468u1	27716a1	87412f1

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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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