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	64	Product of Tamagawa factors cp
Δ	10621255680000000 = 221 · 33 · 57 · 74	Discriminant
Eigenvalues	2- 3+ 5+ 7-  0  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9217633,-10768452863]	[a1,a2,a3,a4,a6]
Generators	[18477:2475200:1]	Generators of the group modulo torsion
j	21145699168383889/2593080	j-invariant
L	5.3295374811792	L(r)(E,1)/r!
Ω	0.086645238355003	Real period
R	3.8443669715459	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	33600cc5 8400ce4 100800mv5 6720cg4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33600ex5

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 33600ex5

-4	8	-3	5
33600cc5	8400ce4	100800mv5	6720cg4

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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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