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	2850t	Isogeny class
Conductor	2850	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-1459200000000 = -1 · 216 · 3 · 58 · 19	Discriminant
Eigenvalues	2- 3+ 5-  0  1 -4 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,987,-56469]	[a1,a2,a3,a4,a6]
Generators	[135:-1668:1]	Generators of the group modulo torsion
j	272199695/3735552	j-invariant
L	4.119064168465	L(r)(E,1)/r!
Ω	0.41685544787674	Real period
R	0.20585993845136	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	22800dn1 91200el1 8550o1 2850h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2850t1

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	1	-4	-4	+	-5	3	-5	6	-2	-4	0	-9	0	-11	1	2	3	17	-3	7	-10

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Quadratic twists for elliptic curve 2850t1

-4	8	-3	5	-19
22800dn1	91200el1	8550o1	2850h1	54150bh1

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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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