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	13200k	Isogeny class
Conductor	13200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	21120	Modular degree for the optimal curve
Δ	-907500000000 = -1 · 28 · 3 · 510 · 112	Discriminant
Eigenvalues	2+ 3+ 5+ -3 11-  5 -6  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-833,47037]	[a1,a2,a3,a4,a6]
j	-25600/363	j-invariant
L	1.4990645364648	L(r)(E,1)/r!
Ω	0.74953226823242	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6600k1 52800gk1 39600r1 13200bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13200k1

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
+	+	+	-3	-	5	-6	1	6	6	5	6	10	-7	4	-2	-12	9	-13	0	2	-12	-2	-6	-1

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Quadratic twists for elliptic curve 13200k1

-4	8	-3	5
6600k1	52800gk1	39600r1	13200bf1

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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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