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	8712s	Isogeny class
Conductor	8712	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	50688	Modular degree for the optimal curve
Δ	11881340006899968 = 28 · 39 · 119	Discriminant
Eigenvalues	2- 3-  2  2 11+ -4 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-91839,-9340958]	[a1,a2,a3,a4,a6]
Generators	[-219:518:1]	Generators of the group modulo torsion
j	194672/27	j-invariant
L	5.1120300997384	L(r)(E,1)/r!
Ω	0.2767731375868	Real period
R	4.6175273224766	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	17424j1 69696bd1 2904e1 8712e1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712s1

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

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Quadratic twists for elliptic curve 8712s1

-4	8	-3	-11
17424j1	69696bd1	2904e1	8712e1

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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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