Cremona's table of elliptic curves

8712 = 2³ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 11-	Signs for the Atkin-Lehner involutions
Class	8712z	Isogeny class
Conductor	8712	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	33792	Modular degree for the optimal curve
Δ	-160018047230976 = -1 · 210 · 36 · 118	Discriminant
Eigenvalues	2- 3- -3  4 11-  3 -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-11979,790614]	[a1,a2,a3,a4,a6]
j	-1188	j-invariant
L	2.1075636391083	L(r)(E,1)/r!
Ω	0.52689090977707	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	17424y1 69696de1 968b1 8712m1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712z1

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
-	-	-3	4	-	3	-3	4	8	5	-4	11	-7	-12	8	1	4	-2	4	-12	10	8	-4	-3	-13

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Quadratic twists for elliptic curve 8712z1

-4	8	-3	-11
17424y1	69696de1	968b1	8712m1

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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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