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	33600fr	Isogeny class
Conductor	33600	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	172032	Modular degree for the optimal curve
Δ	-192849310080000 = -1 · 210 · 316 · 54 · 7	Discriminant
Eigenvalues	2- 3+ 5- 7+  5 -2  4  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-135233,19198137]	[a1,a2,a3,a4,a6]
Generators	[50920:702027:125]	Generators of the group modulo torsion
j	-427361108435200/301327047	j-invariant
L	5.1794382865288	L(r)(E,1)/r!
Ω	0.56125640729874	Real period
R	4.6141462432981	Regulator
r	1	Rank of the group of rational points
S	0.99999999999996	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	33600dy1 8400be1 100800pb1 33600gz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33600fr1

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
-	+	-	+	5	-2	4	6	1	-1	-2	-5	0	-7	2	6	-6	0	3	-9	-12	-3	6	6	-10

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Quadratic twists for elliptic curve 33600fr1

-4	8	-3	5
33600dy1	8400be1	100800pb1	33600gz1

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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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