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	8670x	Isogeny class
Conductor	8670	Conductor
∏ cp	22	Product of Tamagawa factors cp
deg	134640	Modular degree for the optimal curve
Δ	-401803628601600000 = -1 · 211 · 32 · 55 · 178	Discriminant
Eigenvalues	2- 3- 5+  3  1  5 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,12999,30493305]	[a1,a2,a3,a4,a6]
j	34822511/57600000	j-invariant
L	5.1642013294901	L(r)(E,1)/r!
Ω	0.23473642406773	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69360cm1 26010y1 43350o1 8670s1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670x1

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
-	-	+	3	1	5	-	-4	1	-4	8	6	2	-2	9	-3	-11	-2	4	-10	16	-8	-2	-5	-4

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Quadratic twists for elliptic curve 8670x1

-4	-3	5	17
69360cm1	26010y1	43350o1	8670s1

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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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