Cremona's table of elliptic curves

17248 = 2⁵ · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 7- 11+	Signs for the Atkin-Lehner involutions
Class	17248ba	Isogeny class
Conductor	17248	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	43008	Modular degree for the optimal curve
Δ	488894146048 = 29 · 72 · 117	Discriminant
Eigenvalues	2-  3  0 7- 11+ -1  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-20755,1150394]	[a1,a2,a3,a4,a6]
Generators	[-22266:965980:729]	Generators of the group modulo torsion
j	39411764973000/19487171	j-invariant
L	8.6167811467041	L(r)(E,1)/r!
Ω	0.91918319010945	Real period
R	9.3743893920406	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	17248v1 34496bv1 17248w1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 17248ba1

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
-	3	0	-	+	-1	2	-2	-6	-1	4	-2	-2	-8	-6	-8	-1	-5	-9	-4	-10	-9	14	2	-11

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Quadratic twists for elliptic curve 17248ba1

-4	8	-7
17248v1	34496bv1	17248w1

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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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