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	12200d	Isogeny class
Conductor	12200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	-4762880000 = -1 · 211 · 54 · 612	Discriminant
Eigenvalues	2+ -1 5-  2 -3  6  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,392,-1588]	[a1,a2,a3,a4,a6]
j	5191150/3721	j-invariant
L	1.5429586201355	L(r)(E,1)/r!
Ω	0.77147931006777	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24400i1 97600bg1 109800cc1 12200j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12200d1

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
+	-1	-	2	-3	6	3	-5	-4	4	-2	4	9	-4	0	2	-4	+	-5	-14	11	14	1	1	-2

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Quadratic twists for elliptic curve 12200d1

-4	8	-3	5
24400i1	97600bg1	109800cc1	12200j1

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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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