Cremona's table of elliptic curves

2850 = 2 · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 19-	Signs for the Atkin-Lehner involutions
Class	2850r	Isogeny class
Conductor	2850	Conductor
∏ cp	432	Product of Tamagawa factors cp
Δ	-1264250880000000 = -1 · 218 · 32 · 57 · 193	Discriminant
Eigenvalues	2- 3+ 5+ -2  0 -2  0 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,5062,-1702969]	[a1,a2,a3,a4,a6]
Generators	[125:887:1]	Generators of the group modulo torsion
j	918046641959/80912056320	j-invariant
L	3.9709450986998	L(r)(E,1)/r!
Ω	0.23015446626826	Real period
R	0.15975362446493	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	22800cu3 91200cy3 8550l3 570f3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2850r3

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	0	-2	0	-	0	-6	2	-2	0	-8	0	-6	-6	2	4	0	-14	2	-6	-12	10

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Quadratic twists for elliptic curve 2850r3

-4	8	-3	5	-19
22800cu3	91200cy3	8550l3	570f3	54150x3

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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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