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	32	Product of Tamagawa factors cp
Δ	360040606269696 = 28 · 38 · 118	Discriminant
Eigenvalues	2+ 3-  2 -4 11- -6  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-48279,3979690]	[a1,a2,a3,a4,a6]
Generators	[335:5040:1]	Generators of the group modulo torsion
j	37642192/1089	j-invariant
L	4.3040418595563	L(r)(E,1)/r!
Ω	0.53552271246521	Real period
R	4.0185427801402	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	17424u2 69696cx2 2904n2 792e2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712j2

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 8712j2

-4	8	-3	-11
17424u2	69696cx2	2904n2	792e2

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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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