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	12200l	Isogeny class
Conductor	12200	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	30500000000 = 28 · 59 · 61	Discriminant
Eigenvalues	2- -2 5-  0  4  4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-40708,-3174912]	[a1,a2,a3,a4,a6]
Generators	[244:1216:1]	Generators of the group modulo torsion
j	14921197328/61	j-invariant
L	3.4923201853617	L(r)(E,1)/r!
Ω	0.33610798536483	Real period
R	5.1952353669476	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	24400j2 97600bh2 109800w2 12200e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12200l2

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

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Quadratic twists for elliptic curve 12200l2

-4	8	-3	5
24400j2	97600bh2	109800w2	12200e2

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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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