Cremona's table of elliptic curves

1386 = 2 · 3² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	1386c	Isogeny class
Conductor	1386	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1694318472 = 23 · 36 · 74 · 112	Discriminant
Eigenvalues	2+ 3- -2 7+ 11-  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-46473,3867749]	[a1,a2,a3,a4,a6]
Generators	[125:-57:1]	Generators of the group modulo torsion
j	15226621995131793/2324168	j-invariant
L	1.8519655875361	L(r)(E,1)/r!
Ω	1.1697260964094	Real period
R	0.79162360881788	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	11088br3 44352x4 154b3 34650do4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1386c4

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
+	-	-2	+	-	2	-2	0	8	2	-8	-2	-10	4	-8	-6	0	10	-12	-16	-14	0	0	6	10

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Quadratic twists for elliptic curve 1386c4

-4	8	-3	5	-7	-11
11088br3	44352x4	154b3	34650do4	9702w3	15246bv3

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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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