Cremona's table of elliptic curves

5117 = 7 · 17 · 43

Field	Data	Notes
Atkin-Lehner	7+ 17+ 43+	Signs for the Atkin-Lehner involutions
Class	5117a	Isogeny class
Conductor	5117	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	704	Modular degree for the optimal curve
Δ	-1755131 = -1 · 74 · 17 · 43	Discriminant
Eigenvalues	-1 -1 -3 7+  2 -3 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,8,-60]	[a1,a2,a3,a4,a6]
Generators	[8:20:1]	Generators of the group modulo torsion
j	56181887/1755131	j-invariant
L	1.1952887231177	L(r)(E,1)/r!
Ω	1.2778214953464	Real period
R	0.46770567229882	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	81872bd1 46053c1 127925g1 35819i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5117a1

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	-1	-3	+	2	-3	+	2	-2	-6	-6	3	-12	+	13	9	13	11	3	-7	3	8	15	6	2

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Quadratic twists for elliptic curve 5117a1

-4	-3	5	-7	17
81872bd1	46053c1	127925g1	35819i1	86989e1

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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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