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	5117b	Isogeny class
Conductor	5117	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	175978747 = 72 · 174 · 43	Discriminant
Eigenvalues	1  0  0 7+  4  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-187,798]	[a1,a2,a3,a4,a6]
j	725361071625/175978747	j-invariant
L	1.6947227814419	L(r)(E,1)/r!
Ω	1.6947227814419	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	81872y2 46053f2 127925e2 35819j2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5117b2

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

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Quadratic twists for elliptic curve 5117b2

-4	-3	5	-7	17
81872y2	46053f2	127925e2	35819j2	86989f2

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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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