Cremona's table of elliptic curves

8670 = 2 · 3 · 5 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 17+	Signs for the Atkin-Lehner involutions
Class	8670a	Isogeny class
Conductor	8670	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2160	Modular degree for the optimal curve
Δ	-33708960 = -1 · 25 · 36 · 5 · 172	Discriminant
Eigenvalues	2+ 3+ 5+ -1 -1  3 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-48,288]	[a1,a2,a3,a4,a6]
Generators	[3:12:1]	Generators of the group modulo torsion
j	-43713001/116640	j-invariant
L	2.3512089118373	L(r)(E,1)/r!
Ω	1.8283400777461	Real period
R	0.64299003791892	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69360da1 26010br1 43350ct1 8670m1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670a1

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
+	+	+	-1	-1	3	+	4	-7	0	-4	6	-2	2	7	-1	-3	-14	8	-2	8	8	-10	-9	-4

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Quadratic twists for elliptic curve 8670a1

-4	-3	5	17
69360da1	26010br1	43350ct1	8670m1

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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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