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	17248z	Isogeny class
Conductor	17248	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-6377516992 = -1 · 26 · 77 · 112	Discriminant
Eigenvalues	2-  0  0 7- 11+  2 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-245,-4116]	[a1,a2,a3,a4,a6]
Generators	[71:580:1]	Generators of the group modulo torsion
j	-216000/847	j-invariant
L	4.4807063010663	L(r)(E,1)/r!
Ω	0.5510853590724	Real period
R	4.0653468898251	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17248o1 34496bb1 2464l1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 17248z1

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	-	+	2	-4	-2	0	2	10	10	4	-8	6	-2	-4	10	-12	-4	-4	0	14	14	-2

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Quadratic twists for elliptic curve 17248z1

-4	8	-7
17248o1	34496bb1	2464l1

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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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