Cremona's table of elliptic curves

52900 = 2² · 5² · 23²

Field	Data	Notes
Atkin-Lehner	2- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	52900k	Isogeny class
Conductor	52900	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	152064	Modular degree for the optimal curve
Δ	-851206361750000 = -1 · 24 · 56 · 237	Discriminant
Eigenvalues	2- -1 5+  2  0  1 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,22042,-626963]	[a1,a2,a3,a4,a6]
Generators	[11921:145475:343]	Generators of the group modulo torsion
j	32000/23	j-invariant
L	4.7558389654783	L(r)(E,1)/r!
Ω	0.28150428478735	Real period
R	4.2235937625062	Regulator
r	1	Rank of the group of rational points
S	1.0000000000193	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2116c1 2300e1	Quadratic twists by: 5 -23

Hecke Eigenvalues for elliptic curve 52900k1

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	0	1	-6	-2	-	-3	5	8	3	8	-9	6	-12	-14	8	-15	7	10	6	0	-10

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Quadratic twists for elliptic curve 52900k1

5	-23
2116c1	2300e1

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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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