Cremona's table of elliptic curves

1116 = 2² · 3² · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 31+	Signs for the Atkin-Lehner involutions
Class	1116a	Isogeny class
Conductor	1116	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-361584 = -1 · 24 · 36 · 31	Discriminant
Eigenvalues	2- 3- -1  3 -6 -4  0 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-153,729]	[a1,a2,a3,a4,a6]
Generators	[9:-9:1]	Generators of the group modulo torsion
j	-33958656/31	j-invariant
L	2.4944791215006	L(r)(E,1)/r!
Ω	3.0044661274886	Real period
R	0.1383761715422	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4464w1 17856k1 124b1 27900f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1116a1

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
-	-	-1	3	-6	-4	0	-5	4	-2	+	-2	9	2	-4	-12	-9	12	-12	-5	-14	10	-2	-6	-7

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Quadratic twists for elliptic curve 1116a1

-4	8	-3	5	-7	-31
4464w1	17856k1	124b1	27900f1	54684s1	34596k1

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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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