Cremona's table of elliptic curves

5850 = 2 · 3² · 5² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	5850p	Isogeny class
Conductor	5850	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	-11372400000000 = -1 · 210 · 37 · 58 · 13	Discriminant
Eigenvalues	2+ 3- 5+  2 -4 13-  4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-11817,523341]	[a1,a2,a3,a4,a6]
Generators	[34:383:1]	Generators of the group modulo torsion
j	-16022066761/998400	j-invariant
L	3.0658734174961	L(r)(E,1)/r!
Ω	0.70639747831062	Real period
R	1.0850383500902	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	46800ec1 1950x1 1170j1 76050eq1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850p1

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	-4	-	4	-2	2	-8	4	-6	-10	-4	0	6	12	-2	8	0	0	-8	-12	10	8

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Quadratic twists for elliptic curve 5850p1

-4	-3	5	13
46800ec1	1950x1	1170j1	76050eq1

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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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