Cremona's table of elliptic curves

59200 = 2⁶ · 5² · 37

Field	Data	Notes
Atkin-Lehner	2- 5+ 37-	Signs for the Atkin-Lehner involutions
Class	59200cu	Isogeny class
Conductor	59200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	925000000 = 26 · 58 · 37	Discriminant
Eigenvalues	2-  1 5+ -3 -5  4  4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-533,-4687]	[a1,a2,a3,a4,a6]
Generators	[-16:1:1]	Generators of the group modulo torsion
j	16777216/925	j-invariant
L	5.2987384763435	L(r)(E,1)/r!
Ω	0.99687221169694	Real period
R	2.6576819045364	Regulator
r	1	Rank of the group of rational points
S	1.0000000000036	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59200z1 14800m1 11840x1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 59200cu1

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	+	-3	-5	4	4	-8	4	-4	-2	-	-5	6	9	3	-8	10	4	-5	15	14	-11	-2	-10

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Quadratic twists for elliptic curve 59200cu1

-4	8	5
59200z1	14800m1	11840x1

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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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