Cremona's table of elliptic curves

12200 = 2³ · 5² · 61

Field	Data	Notes
Atkin-Lehner	2- 5- 61+	Signs for the Atkin-Lehner involutions
Class	12200k	Isogeny class
Conductor	12200	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-476288000 = -1 · 210 · 53 · 612	Discriminant
Eigenvalues	2-  0 5-  0  6 -4  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,5,-1050]	[a1,a2,a3,a4,a6]
Generators	[14:42:1]	Generators of the group modulo torsion
j	108/3721	j-invariant
L	4.6782398217892	L(r)(E,1)/r!
Ω	0.76556527823017	Real period
R	3.0554153609241	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	24400h2 97600be2 109800x2 12200c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12200k2

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

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Quadratic twists for elliptic curve 12200k2

-4	8	-3	5
24400h2	97600be2	109800x2	12200c2

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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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