Cremona's table of elliptic curves

13200 = 2⁴ · 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 11-	Signs for the Atkin-Lehner involutions
Class	13200bu	Isogeny class
Conductor	13200	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	33792000000 = 216 · 3 · 56 · 11	Discriminant
Eigenvalues	2- 3+ 5+ -4 11-  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-808,112]	[a1,a2,a3,a4,a6]
Generators	[-3:50:1]	Generators of the group modulo torsion
j	912673/528	j-invariant
L	3.5050841858447	L(r)(E,1)/r!
Ω	0.98121333208872	Real period
R	1.7860969022829	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	1650f1 52800gp1 39600do1 528j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13200bu1

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

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Quadratic twists for elliptic curve 13200bu1

-4	8	-3	5
1650f1	52800gp1	39600do1	528j1

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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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