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	59200a	Isogeny class
Conductor	59200	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	560742400000000 = 220 · 58 · 372	Discriminant
Eigenvalues	2+  0 5+  0  4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-40300,-2898000]	[a1,a2,a3,a4,a6]
Generators	[-300703:-509703:2197]	Generators of the group modulo torsion
j	1767172329/136900	j-invariant
L	6.7981521459842	L(r)(E,1)/r!
Ω	0.33860933859493	Real period
R	10.038341195982	Regulator
r	1	Rank of the group of rational points
S	1.0000000000089	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	59200bx2 1850j2 11840o2	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 59200a2

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

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Quadratic twists for elliptic curve 59200a2

-4	8	5
59200bx2	1850j2	11840o2

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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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