Cremona's table of elliptic curves

186 = 2 · 3 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 31+	Signs for the Atkin-Lehner involutions
Class	186c	Isogeny class
Conductor	186	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	28	Modular degree for the optimal curve
Δ	-11904 = -1 · 27 · 3 · 31	Discriminant
Eigenvalues	2+ 3-  3 -2  5 -7 -1  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-17,-28]	[a1,a2,a3,a4,a6]
j	-498677257/11904	j-invariant
L	1.1823572974903	L(r)(E,1)/r!
Ω	1.1823572974903	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	1488k1 5952e1 558g1 4650y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 186c1

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
+	-	3	-2	5	-7	-1	7	4	-8	+	-6	-2	-10	-1	6	-10	1	-3	3	14	-11	7	-6	-3

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Quadratic twists for elliptic curve 186c1

-4	8	-3	5	-7	-11	13	17	-19	-23	-31
1488k1	5952e1	558g1	4650y1	9114j1	22506bi1	31434x1	53754c1	67146i1	98394ba1	5766c1

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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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