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	8712j	Isogeny class
Conductor	8712	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	43641285608448 = 210 · 37 · 117	Discriminant
Eigenvalues	2+ 3-  2 -4 11- -6  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-767019,258557398]	[a1,a2,a3,a4,a6]
Generators	[231:9680:1]	Generators of the group modulo torsion
j	37736227588/33	j-invariant
L	4.3040418595563	L(r)(E,1)/r!
Ω	0.53552271246521	Real period
R	2.0092713900701	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17424u3 69696cx4 2904n3 792e3	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712j4

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
+	-	2	-4	-	-6	6	8	0	-6	0	6	-10	8	0	-6	-4	2	-12	8	-2	4	-12	6	2

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Quadratic twists for elliptic curve 8712j4

-4	8	-3	-11
17424u3	69696cx4	2904n3	792e3

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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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