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	16	Product of Tamagawa factors cp
Δ	8750986957944 = 23 · 36 · 7 · 118	Discriminant
Eigenvalues	2+ 3- -2 7+ 11-  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5433,-57835]	[a1,a2,a3,a4,a6]
Generators	[-37:321:1]	Generators of the group modulo torsion
j	24331017010833/12004097336	j-invariant
L	1.8519655875361	L(r)(E,1)/r!
Ω	0.58486304820469	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	11088br4 44352x3 154b4 34650do3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1386c3

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 1386c3

-4	8	-3	5	-7	-11
11088br4	44352x3	154b4	34650do3	9702w4	15246bv4

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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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