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	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-527175090288 = -1 · 24 · 38 · 73 · 114	Discriminant
Eigenvalues	2+ 3- -2 7+ 11+ -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-873,-36099]	[a1,a2,a3,a4,a6]
j	-100999381393/723148272	j-invariant
L	0.77842268575899	L(r)(E,1)/r!
Ω	0.38921134287949	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11088ca1 44352bk1 462f1 34650di1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1386b1

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 1386b1

-4	8	-3	5	-7	-11
11088ca1	44352bk1	462f1	34650di1	9702p1	15246bu1

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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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