Cremona's table of elliptic curves

33200 = 2⁴ · 5² · 83

Field	Data	Notes
Atkin-Lehner	2+ 5+ 83+	Signs for the Atkin-Lehner involutions
Class	33200a	Isogeny class
Conductor	33200	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-33200000000 = -1 · 210 · 58 · 83	Discriminant
Eigenvalues	2+  1 5+  1 -3  4  5  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-408,9188]	[a1,a2,a3,a4,a6]
Generators	[-2:100:1]	Generators of the group modulo torsion
j	-470596/2075	j-invariant
L	7.0112717625088	L(r)(E,1)/r!
Ω	1.0148873313922	Real period
R	0.86355297105874	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16600j1 6640b1	Quadratic twists by: -4 5

Hecke Eigenvalues for elliptic curve 33200a1

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
+	1	+	1	-3	4	5	0	8	-5	-3	3	-6	6	-8	-4	-5	-13	-10	16	8	-10	+	-12	2

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Quadratic twists for elliptic curve 33200a1

-4	5
16600j1	6640b1

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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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