Cremona's table of elliptic curves

33600 = 2⁶ · 3 · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7-	Signs for the Atkin-Lehner involutions
Class	33600ex	Isogeny class
Conductor	33600	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	8429568000000000 = 222 · 3 · 59 · 73	Discriminant
Eigenvalues	2- 3+ 5+ 7-  0  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4289633,3421051137]	[a1,a2,a3,a4,a6]
Generators	[1152:2625:1]	Generators of the group modulo torsion
j	2131200347946769/2058000	j-invariant
L	5.3295374811792	L(r)(E,1)/r!
Ω	0.34658095342001	Real period
R	1.281455657182	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	33600cc3 8400ce3 100800mv3 6720cg3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33600ex3

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
-	+	+	-	0	2	6	-4	0	6	4	2	6	-8	-12	6	-12	-2	-8	0	-14	16	-12	6	-14

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Quadratic twists for elliptic curve 33600ex3

-4	8	-3	5
33600cc3	8400ce3	100800mv3	6720cg3

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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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