Cremona's table of elliptic curves

3636 = 2² · 3² · 101

Field	Data	Notes
Atkin-Lehner	2- 3- 101+	Signs for the Atkin-Lehner involutions
Class	3636a	Isogeny class
Conductor	3636	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	18849024 = 28 · 36 · 101	Discriminant
Eigenvalues	2- 3-  1 -2  2 -3  1  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-72,-108]	[a1,a2,a3,a4,a6]
Generators	[-3:9:1]	Generators of the group modulo torsion
j	221184/101	j-invariant
L	3.5863241261468	L(r)(E,1)/r!
Ω	1.7114648113068	Real period
R	1.0477352798766	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	14544q1 58176ba1 404a1 90900e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3636a1

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
-	-	1	-2	2	-3	1	1	-3	2	-3	-2	-2	4	3	0	-12	-10	2	1	2	1	-4	6	-2

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Quadratic twists for elliptic curve 3636a1

-4	8	-3	5
14544q1	58176ba1	404a1	90900e1

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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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