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	5170b	Isogeny class
Conductor	5170	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2112	Modular degree for the optimal curve
Δ	-156392500 = -1 · 22 · 54 · 113 · 47	Discriminant
Eigenvalues	2+ -2 5+ -1 11- -5 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,21,602]	[a1,a2,a3,a4,a6]
Generators	[-7:14:1] [1:24:1]	Generators of the group modulo torsion
j	1095912791/156392500	j-invariant
L	2.6678455755629	L(r)(E,1)/r!
Ω	1.4030781211792	Real period
R	0.15845195023309	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41360h1 46530bc1 25850m1 56870q1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 5170b1

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	+	-1	-	-5	-4	-4	-7	-2	1	-7	-3	-10	+	5	-10	10	-5	0	6	1	-15	-3	-3

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Quadratic twists for elliptic curve 5170b1

-4	-3	5	-11
41360h1	46530bc1	25850m1	56870q1

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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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