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	59200cv	Isogeny class
Conductor	59200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	37000000 = 26 · 56 · 37	Discriminant
Eigenvalues	2- -1 5+ -1  3 -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-333,-2213]	[a1,a2,a3,a4,a6]
Generators	[22:25:1]	Generators of the group modulo torsion
j	4096000/37	j-invariant
L	4.1636289833151	L(r)(E,1)/r!
Ω	1.1179351468711	Real period
R	1.8621961189024	Regulator
r	1	Rank of the group of rational points
S	0.99999999998538	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59200x1 14800l1 2368j1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 59200cv1

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	+	-1	3	-4	-6	2	6	6	4	-	-9	-8	3	-3	12	-8	4	15	-11	10	-9	6	-8

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Quadratic twists for elliptic curve 59200cv1

-4	8	5
59200x1	14800l1	2368j1

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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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