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	8670c	Isogeny class
Conductor	8670	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	957238056374400 = 27 · 36 · 52 · 177	Discriminant
Eigenvalues	2+ 3+ 5+  2 -4  0 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3353128,-2364721472]	[a1,a2,a3,a4,a6]
Generators	[8331:736108:1]	Generators of the group modulo torsion
j	172735174415217961/39657600	j-invariant
L	2.5016689210321	L(r)(E,1)/r!
Ω	0.11156732254074	Real period
R	5.6057384547314	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	69360dd2 26010bu2 43350db2 510b2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670c2

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	-4	0	+	4	-4	-6	8	6	-8	2	-8	14	6	-2	2	10	-4	-4	-16	6	8

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Quadratic twists for elliptic curve 8670c2

-4	-3	5	17
69360dd2	26010bu2	43350db2	510b2

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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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