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
deg	576	Modular degree for the optimal curve
Δ	678984768 = 26 · 39 · 72 · 11	Discriminant
Eigenvalues	2+ 3+  2 7+ 11+ -4  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-231,-451]	[a1,a2,a3,a4,a6]
Generators	[-10:33:1]	Generators of the group modulo torsion
j	69426531/34496	j-invariant
L	2.1962233198986	L(r)(E,1)/r!
Ω	1.2887415247107	Real period
R	0.85208060646283	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	11088bd1 44352d1 1386f1 34650cp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1386a1

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 1386a1

-4	8	-3	5	-7	-11
11088bd1	44352d1	1386f1	34650cp1	9702h1	15246bc1

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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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