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	2132c	Isogeny class
Conductor	2132	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-136448 = -1 · 28 · 13 · 41	Discriminant
Eigenvalues	2-  3  0 -2  0 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-55,158]	[a1,a2,a3,a4,a6]
j	-71874000/533	j-invariant
L	3.2957816856676	L(r)(E,1)/r!
Ω	3.2957816856676	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8528j1 34112c1 19188p1 53300b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2132c1

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	0	-	-2	4	6	10	5	6	-	2	-6	6	3	3	-2	-8	-4	0	-9	-9	5

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Quadratic twists for elliptic curve 2132c1

-4	8	-3	5	-7	13	41
8528j1	34112c1	19188p1	53300b1	104468n1	27716b1	87412a1

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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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