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	2850b	Isogeny class
Conductor	2850	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	7635996093750 = 2 · 3 · 510 · 194	Discriminant
Eigenvalues	2+ 3+ 5+ -4 -4  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-5500,81250]	[a1,a2,a3,a4,a6]
Generators	[9:176:1]	Generators of the group modulo torsion
j	1177918188481/488703750	j-invariant
L	1.801588555832	L(r)(E,1)/r!
Ω	0.67104339386443	Real period
R	1.3423785796153	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	22800dk3 91200ed3 8550ba4 570m3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2850b3

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
+	+	+	-4	-4	2	2	+	8	6	4	10	-2	-12	0	-6	0	-10	4	-8	-2	-12	8	6	-18

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Quadratic twists for elliptic curve 2850b3

-4	8	-3	5	-19
22800dk3	91200ed3	8550ba4	570m3	54150ct3

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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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