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	8670s	Isogeny class
Conductor	8670	Conductor
∏ cp	110	Product of Tamagawa factors cp
deg	7920	Modular degree for the optimal curve
Δ	-16646400000 = -1 · 211 · 32 · 55 · 172	Discriminant
Eigenvalues	2- 3+ 5- -3 -1  5 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,45,6225]	[a1,a2,a3,a4,a6]
Generators	[43:-322:1]	Generators of the group modulo torsion
j	34822511/57600000	j-invariant
L	5.4600253615838	L(r)(E,1)/r!
Ω	0.96784307061104	Real period
R	0.051285787648279	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	69360dt1 26010n1 43350be1 8670x1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670s1

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 8670s1

-4	-3	5	17
69360dt1	26010n1	43350be1	8670x1

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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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