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	2850n	Isogeny class
Conductor	2850	Conductor
∏ cp	28	Product of Tamagawa factors cp
Δ	22719102750 = 2 · 314 · 53 · 19	Discriminant
Eigenvalues	2+ 3- 5-  0 -4  4 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-786,4318]	[a1,a2,a3,a4,a6]
Generators	[-28:81:1]	Generators of the group modulo torsion
j	428831641421/181752822	j-invariant
L	2.8916625749342	L(r)(E,1)/r!
Ω	1.0874093844016	Real period
R	0.3798888068171	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	22800cp2 91200ca2 8550bk2 2850v2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2850n2

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

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Quadratic twists for elliptic curve 2850n2

-4	8	-3	5	-19
22800cp2	91200ca2	8550bk2	2850v2	54150cd2

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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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