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	8670b	Isogeny class
Conductor	8670	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3.0017556238303E+19	Discriminant
Eigenvalues	2+ 3+ 5+  2  0  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-785363,-48068283]	[a1,a2,a3,a4,a6]
Generators	[2027987:7370069:2197]	Generators of the group modulo torsion
j	451747330217/253125000	j-invariant
L	2.7577956350521	L(r)(E,1)/r!
Ω	0.17236492924067	Real period
R	7.9998745893416	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	69360dc2 26010bs2 43350cz2 8670k2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670b2

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

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Quadratic twists for elliptic curve 8670b2

-4	-3	5	17
69360dc2	26010bs2	43350cz2	8670k2

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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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