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	8712i	Isogeny class
Conductor	8712	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-592628990976 = -1 · 210 · 314 · 112	Discriminant
Eigenvalues	2+ 3-  1  0 11-  1  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2013,12782]	[a1,a2,a3,a4,a6]
Generators	[31:324:1]	Generators of the group modulo torsion
j	9987164/6561	j-invariant
L	4.7305550976743	L(r)(E,1)/r!
Ω	0.57438600074877	Real period
R	2.0589616962755	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	17424r1 69696bs1 2904j1 8712x1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712i1

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	0	-	1	3	0	-4	-1	0	-1	-9	-4	4	-3	-12	-14	16	12	-10	-4	0	5	-5

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Quadratic twists for elliptic curve 8712i1

-4	8	-3	-11
17424r1	69696bs1	2904j1	8712x1

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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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