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	1386a	Isogeny class
Conductor	1386	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-45746598744 = -1 · 23 · 39 · 74 · 112	Discriminant
Eigenvalues	2+ 3+  2 7+ 11+ -4  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,849,-4123]	[a1,a2,a3,a4,a6]
Generators	[17:114:1]	Generators of the group modulo torsion
j	3436115229/2324168	j-invariant
L	2.1962233198986	L(r)(E,1)/r!
Ω	0.64437076235534	Real period
R	1.7041612129257	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	11088bd2 44352d2 1386f2 34650cp2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1386a2

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

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Quadratic twists for elliptic curve 1386a2

-4	8	-3	5	-7	-11
11088bd2	44352d2	1386f2	34650cp2	9702h2	15246bc2

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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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