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	13200cc	Isogeny class
Conductor	13200	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	4783214700000000 = 28 · 33 · 58 · 116	Discriminant
Eigenvalues	2- 3- 5+  2 11+ -2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-78908,7829688]	[a1,a2,a3,a4,a6]
Generators	[2234:22125:8]	Generators of the group modulo torsion
j	13584145739344/1195803675	j-invariant
L	5.9853612584711	L(r)(E,1)/r!
Ω	0.42254617216526	Real period
R	4.721662509133	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	3300e2 52800ev2 39600dv2 2640o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13200cc2

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

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Quadratic twists for elliptic curve 13200cc2

-4	8	-3	5
3300e2	52800ev2	39600dv2	2640o2

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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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