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	1386b	Isogeny class
Conductor	1386	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	36092284074 = 2 · 314 · 73 · 11	Discriminant
Eigenvalues	2+ 3- -2 7+ 11+ -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-362223,-83819205]	[a1,a2,a3,a4,a6]
j	7209828390823479793/49509306	j-invariant
L	0.77842268575899	L(r)(E,1)/r!
Ω	0.19460567143975	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11088ca4 44352bk4 462f4 34650di4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1386b3

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

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Quadratic twists for elliptic curve 1386b3

-4	8	-3	5	-7	-11
11088ca4	44352bk4	462f4	34650di4	9702p4	15246bu4

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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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