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	8670i	Isogeny class
Conductor	8670	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	4320	Modular degree for the optimal curve
Δ	-7022700 = -1 · 22 · 35 · 52 · 172	Discriminant
Eigenvalues	2+ 3- 5+ -3 -6 -7 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-134,596]	[a1,a2,a3,a4,a6]
Generators	[-9:37:1] [174:-811:8]	Generators of the group modulo torsion
j	-910904761/24300	j-invariant
L	4.4340500832413	L(r)(E,1)/r!
Ω	2.3547894492649	Real period
R	0.094149608251128	Regulator
r	2	Rank of the group of rational points
S	0.99999999999951	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69360cg1 26010by1 43350ce1 8670f1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670i1

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	-6	-7	+	-5	-8	0	5	-3	10	-5	-12	2	-6	-5	-7	-8	-6	8	-14	-4	13

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Quadratic twists for elliptic curve 8670i1

-4	-3	5	17
69360cg1	26010by1	43350ce1	8670f1

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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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