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	8712m	Isogeny class
Conductor	8712	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-90326016 = -1 · 210 · 36 · 112	Discriminant
Eigenvalues	2+ 3- -3 -4 11- -3  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-99,-594]	[a1,a2,a3,a4,a6]
Generators	[15:36:1]	Generators of the group modulo torsion
j	-1188	j-invariant
L	2.701478822792	L(r)(E,1)/r!
Ω	0.73077581675038	Real period
R	0.92418179449513	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	17424x1 69696df1 968d1 8712z1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712m1

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 8712m1

-4	8	-3	-11
17424x1	69696df1	968d1	8712z1

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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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