Cremona's table of elliptic curves

1862 = 2 · 7² · 19

Field	Data	Notes
Atkin-Lehner	2+ 7- 19+	Signs for the Atkin-Lehner involutions
Class	1862b	Isogeny class
Conductor	1862	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-300021048147968 = -1 · 227 · 76 · 19	Discriminant
Eigenvalues	2+ -1  0 7- -6 -5 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-4190,838132]	[a1,a2,a3,a4,a6]
j	-69173457625/2550136832	j-invariant
L	0.45455056676453	L(r)(E,1)/r!
Ω	0.45455056676453	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14896bd3 59584bg3 16758bc3 46550ca3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1862b3

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
+	-1	0	-	-6	-5	-3	+	3	9	4	2	0	8	0	-3	-9	10	5	-6	7	-10	6	12	10

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Quadratic twists for elliptic curve 1862b3

-4	8	-3	5	-7	-19
14896bd3	59584bg3	16758bc3	46550ca3	38a2	35378o3

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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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