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	2850w	Isogeny class
Conductor	2850	Conductor
∏ cp	150	Product of Tamagawa factors cp
deg	7200	Modular degree for the optimal curve
Δ	-6979308364800 = -1 · 210 · 315 · 52 · 19	Discriminant
Eigenvalues	2- 3- 5+ -2 -3 -6 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,4772,7952]	[a1,a2,a3,a4,a6]
Generators	[26:374:1]	Generators of the group modulo torsion
j	480705753733655/279172334592	j-invariant
L	5.1364621569963	L(r)(E,1)/r!
Ω	0.44954163067819	Real period
R	1.9043331423489	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	22800cd1 91200bg1 8550e1 2850g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2850w1

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	-3	-6	-2	+	-1	-5	7	-2	2	-6	-12	9	-10	-13	-7	12	9	5	-1	5	-12

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Quadratic twists for elliptic curve 2850w1

-4	8	-3	5	-19
22800cd1	91200bg1	8550e1	2850g2	54150h1

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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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