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	13200j	Isogeny class
Conductor	13200	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	992351250000 = 24 · 38 · 57 · 112	Discriminant
Eigenvalues	2+ 3+ 5+ -2 11-  4  4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-273283,55079062]	[a1,a2,a3,a4,a6]
j	9028656748079104/3969405	j-invariant
L	1.4320031446535	L(r)(E,1)/r!
Ω	0.71600157232675	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6600j1 52800gi1 39600p1 2640h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13200j1

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
+	+	+	-2	-	4	4	-8	4	2	-8	2	-2	-6	12	-6	12	10	16	0	-4	-12	-6	6	-14

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Quadratic twists for elliptic curve 13200j1

-4	8	-3	5
6600j1	52800gi1	39600p1	2640h1

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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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