Cremona's table of elliptic curves

9471 = 3 · 7 · 11 · 41

Field	Data	Notes
Atkin-Lehner	3+ 7+ 11+ 41+	Signs for the Atkin-Lehner involutions
Class	9471a	Isogeny class
Conductor	9471	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	89699841 = 32 · 72 · 112 · 412	Discriminant
Eigenvalues	1 3+  2 7+ 11+  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-289,1720]	[a1,a2,a3,a4,a6]
Generators	[-8:64:1]	Generators of the group modulo torsion
j	2683880485273/89699841	j-invariant
L	4.7946240396368	L(r)(E,1)/r!
Ω	1.8976691241963	Real period
R	2.5265858934536	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	28413d2 66297n2 104181k2	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 9471a2

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
1	+	2	+	+	2	-2	4	-4	-2	0	6	+	12	0	-10	4	2	0	-16	-2	-8	-4	-14	14

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Quadratic twists for elliptic curve 9471a2

-3	-7	-11
28413d2	66297n2	104181k2

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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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