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	186a	Isogeny class
Conductor	186	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	44	Modular degree for the optimal curve
Δ	-10983114 = -1 · 2 · 311 · 31	Discriminant
Eigenvalues	2+ 3+ -1  2  3  3  1  7	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-83,-369]	[a1,a2,a3,a4,a6]
j	-64432972729/10983114	j-invariant
L	0.78233545936944	L(r)(E,1)/r!
Ω	0.78233545936944	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	1488n1 5952r1 558h1 4650bm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 186a1

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	2	3	3	1	7	0	4	-	-10	-6	6	-5	-2	6	3	-3	7	-10	-1	17	6	5

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Quadratic twists for elliptic curve 186a1

-4	8	-3	5	-7	-11	13	17	-19	-23	-31
1488n1	5952r1	558h1	4650bm1	9114k1	22506bb1	31434m1	53754f1	67146k1	98394g1	5766e1

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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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