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	8712k	Isogeny class
Conductor	8712	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	2356629422856192 = 211 · 310 · 117	Discriminant
Eigenvalues	2+ 3- -2  0 11- -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-514371,141972446]	[a1,a2,a3,a4,a6]
Generators	[1606:58806:1]	Generators of the group modulo torsion
j	5690357426/891	j-invariant
L	3.7233681670076	L(r)(E,1)/r!
Ω	0.44459231109581	Real period
R	2.0936980206824	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	17424v3 69696cd4 2904k3 792d3	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712k3

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	0	-	-2	6	0	-4	2	0	-10	6	8	4	6	12	-2	4	-12	14	-16	-12	-10	-14

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Quadratic twists for elliptic curve 8712k3

-4	8	-3	-11
17424v3	69696cd4	2904k3	792d3

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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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