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	59200dn	Isogeny class
Conductor	59200	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	7296	Modular degree for the optimal curve
Δ	-1480000 = -1 · 26 · 54 · 37	Discriminant
Eigenvalues	2-  2 5-  2  2 -4  4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,62]	[a1,a2,a3,a4,a6]
Generators	[201:512:27]	Generators of the group modulo torsion
j	-1600/37	j-invariant
L	10.078570236883	L(r)(E,1)/r!
Ω	2.2548408697461	Real period
R	4.4697478975661	Regulator
r	1	Rank of the group of rational points
S	0.99999999999892	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59200dp1 29600n1 59200df1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 59200dn1

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	2	-4	4	-1	1	4	0	+	-5	-1	-6	5	-11	-10	-8	14	-13	-3	12	-12	-14

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Quadratic twists for elliptic curve 59200dn1

-4	8	5
59200dp1	29600n1	59200df1

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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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