Cremona's table of elliptic curves

5170 = 2 · 5 · 11 · 47

Field	Data	Notes
Atkin-Lehner	2+ 5+ 11+ 47-	Signs for the Atkin-Lehner involutions
Class	5170a	Isogeny class
Conductor	5170	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	10340000 = 25 · 54 · 11 · 47	Discriminant
Eigenvalues	2+  0 5+  0 11+ -6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-88235,-10066075]	[a1,a2,a3,a4,a6]
j	75971228776233442569/10340000	j-invariant
L	0.55401190482602	L(r)(E,1)/r!
Ω	0.27700595241301	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	41360i4 46530bg4 25850h4 56870s4	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 5170a3

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

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Quadratic twists for elliptic curve 5170a3

-4	-3	5	-11
41360i4	46530bg4	25850h4	56870s4

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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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