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	33600ge	Isogeny class
Conductor	33600	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	914457600000000 = 216 · 36 · 58 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+  4 -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-33633,1864863]	[a1,a2,a3,a4,a6]
Generators	[-81:2016:1]	Generators of the group modulo torsion
j	4108974916/893025	j-invariant
L	7.3628441346795	L(r)(E,1)/r!
Ω	0.46969088864818	Real period
R	1.3063279688532	Regulator
r	1	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	33600bd2 8400d2 100800md2 6720bt2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33600ge2

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
-	-	+	+	4	-2	6	0	0	6	0	-6	-10	0	-12	-6	-4	-2	-8	4	-10	0	-12	-10	14

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Quadratic twists for elliptic curve 33600ge2

-4	8	-3	5
33600bd2	8400d2	100800md2	6720bt2

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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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