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	33600gg	Isogeny class
Conductor	33600	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	3292047360000000 = 217 · 38 · 57 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1048033,412604063]	[a1,a2,a3,a4,a6]
Generators	[53:18900:1]	Generators of the group modulo torsion
j	62161150998242/1607445	j-invariant
L	5.849263425772	L(r)(E,1)/r!
Ω	0.4148907950802	Real period
R	0.88114503490024	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	33600x6 8400c5 100800lw6 6720bm5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33600gg6

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	-2	-4	0	10	0	6	-6	4	-8	6	-4	10	-4	16	14	-8	4	10	-10

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Quadratic twists for elliptic curve 33600gg6

-4	8	-3	5
33600x6	8400c5	100800lw6	6720bm5

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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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