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	1116c	Isogeny class
Conductor	1116	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-3254256 = -1 · 24 · 38 · 31	Discriminant
Eigenvalues	2- 3-  1 -1  0 -6  8  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-57,-187]	[a1,a2,a3,a4,a6]
j	-1755904/279	j-invariant
L	1.7224768514925	L(r)(E,1)/r!
Ω	0.86123842574627	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4464q1 17856ba1 372a1 27900j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1116c1

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	-1	0	-6	8	7	6	8	-	8	-9	0	8	-4	-3	0	12	5	-4	14	-2	6	-7

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Quadratic twists for elliptic curve 1116c1

-4	8	-3	5	-7	-31
4464q1	17856ba1	372a1	27900j1	54684l1	34596h1

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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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