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	186b	Isogeny class
Conductor	186	Conductor
∏ cp	5	Product of Tamagawa factors cp
Δ	-171774906 = -1 · 2 · 3 · 315	Discriminant
Eigenvalues	2- 3-  1 -2 -3 -1  3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1395,-20181]	[a1,a2,a3,a4,a6]
j	-300238092661681/171774906	j-invariant
L	1.9528976689997	L(r)(E,1)/r!
Ω	0.39057953379994	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	1488h2 5952f2 558d2 4650e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 186b2

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	-1	3	-5	4	0	-	-2	2	-6	-7	14	10	7	-7	-3	-6	15	-1	10	13

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Quadratic twists for elliptic curve 186b2

-4	8	-3	5	-7	-11	13	17	-19	-23	-31
1488h2	5952f2	558d2	4650e2	9114r2	22506p2	31434g2	53754i2	67146a2	98394bq2	5766g2

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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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