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	8712n	Isogeny class
Conductor	8712	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	322560	Modular degree for the optimal curve
Δ	31814497208558592 = 210 · 313 · 117	Discriminant
Eigenvalues	2+ 3- -4  2 11-  0 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8729787,-9927809210]	[a1,a2,a3,a4,a6]
Generators	[-1416601714:-47285469:830584]	Generators of the group modulo torsion
j	55635379958596/24057	j-invariant
L	3.3470315298314	L(r)(E,1)/r!
Ω	0.087831167182078	Real period
R	9.52689016102	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	17424z1 69696do1 2904o1 792g1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712n1

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

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Quadratic twists for elliptic curve 8712n1

-4	8	-3	-11
17424z1	69696do1	2904o1	792g1

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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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