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	8670q	Isogeny class
Conductor	8670	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	5601996415417082400 = 25 · 310 · 52 · 179	Discriminant
Eigenvalues	2- 3+ 5-  0  4  0 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-714125,202152035]	[a1,a2,a3,a4,a6]
Generators	[33:13348:1]	Generators of the group modulo torsion
j	339630096833/47239200	j-invariant
L	6.0738827419998	L(r)(E,1)/r!
Ω	0.23125223135247	Real period
R	2.6265185449139	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	69360dp2 26010g2 43350z2 8670u2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670q2

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

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Quadratic twists for elliptic curve 8670q2

-4	-3	5	17
69360dp2	26010g2	43350z2	8670u2

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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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