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	12	Product of Tamagawa factors cp
Δ	-72726784 = -1 · 28 · 132 · 412	Discriminant
Eigenvalues	2- -2  2  4  0 13+ -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-172,-1020]	[a1,a2,a3,a4,a6]
Generators	[28:130:1]	Generators of the group modulo torsion
j	-2211014608/284089	j-invariant
L	2.7058387996085	L(r)(E,1)/r!
Ω	0.65414243755495	Real period
R	1.3788224318658	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	8528h2 34112k2 19188k2 53300g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2132b2

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 2132b2

-4	8	-3	5	-7	13	41
8528h2	34112k2	19188k2	53300g2	104468u2	27716a2	87412f2

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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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