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	13200z	Isogeny class
Conductor	13200	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	12251250000 = 24 · 34 · 57 · 112	Discriminant
Eigenvalues	2+ 3- 5+ -2 11-  4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3283,-73312]	[a1,a2,a3,a4,a6]
Generators	[68:150:1]	Generators of the group modulo torsion
j	15657723904/49005	j-invariant
L	5.5149335671439	L(r)(E,1)/r!
Ω	0.63081574863441	Real period
R	2.1856356547386	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	6600c1 52800ek1 39600o1 2640d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13200z1

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	0	-4	-6	8	2	-10	10	-12	-6	12	10	-8	0	-4	-4	2	-10	2

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Quadratic twists for elliptic curve 13200z1

-4	8	-3	5
6600c1	52800ek1	39600o1	2640d1

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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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