Cremona's table of elliptic curves

36600 = 2³ · 3 · 5² · 61

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 61+	Signs for the Atkin-Lehner involutions
Class	36600s	Isogeny class
Conductor	36600	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	6028020000000 = 28 · 34 · 57 · 612	Discriminant
Eigenvalues	2- 3+ 5+ -2 -4  2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-54508,4915012]	[a1,a2,a3,a4,a6]
Generators	[157:-450:1] [-168:3050:1]	Generators of the group modulo torsion
j	4477673574736/1507005	j-invariant
L	7.312505818269	L(r)(E,1)/r!
Ω	0.74117805601064	Real period
R	0.61662863590673	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	73200u2 109800m2 7320e2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 36600s2

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	-4	2	4	-4	-6	-6	-4	-8	-10	6	-12	-12	-12	+	10	0	10	-4	-12	-2	6

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Quadratic twists for elliptic curve 36600s2

-4	-3	5
73200u2	109800m2	7320e2

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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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