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	2850u	Isogeny class
Conductor	2850	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-21888000 = -1 · 210 · 32 · 53 · 19	Discriminant
Eigenvalues	2- 3+ 5-  0 -4  2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-158,731]	[a1,a2,a3,a4,a6]
Generators	[9:-17:1]	Generators of the group modulo torsion
j	-3491055413/175104	j-invariant
L	4.0811066681798	L(r)(E,1)/r!
Ω	2.1232825451836	Real period
R	0.19220742323895	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	22800do1 91200em1 8550p1 2850m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2850u1

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
-	+	-	0	-4	2	-6	+	6	-2	-6	-10	0	-6	6	10	2	-6	8	-12	-16	-14	12	4	-10

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Quadratic twists for elliptic curve 2850u1

-4	8	-3	5	-19
22800do1	91200em1	8550p1	2850m1	54150bi1

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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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