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	2850k	Isogeny class
Conductor	2850	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	846093750 = 2 · 3 · 58 · 192	Discriminant
Eigenvalues	2+ 3- 5+  2  0 -6 -8 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-751,-7852]	[a1,a2,a3,a4,a6]
Generators	[42:166:1]	Generators of the group modulo torsion
j	2992209121/54150	j-invariant
L	3.0017511609822	L(r)(E,1)/r!
Ω	0.91313697591822	Real period
R	1.6436477988221	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	22800br2 91200c2 8550bc2 570h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2850k2

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

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Quadratic twists for elliptic curve 2850k2

-4	8	-3	5	-19
22800br2	91200c2	8550bc2	570h2	54150bw2

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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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