Cremona's table of elliptic curves

9248 = 2⁵ · 17²

Field	Data	Notes
Atkin-Lehner	2- 17+	Signs for the Atkin-Lehner involutions
Class	9248g	Isogeny class
Conductor	9248	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1024	Modular degree for the optimal curve
Δ	314432 = 26 · 173	Discriminant
Eigenvalues	2-  0 -4  0  0 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-17,0]	[a1,a2,a3,a4,a6]
Generators	[-4:2:1] [-1:4:1]	Generators of the group modulo torsion
j	1728	j-invariant
L	4.7953484875916	L(r)(E,1)/r!
Ω	2.582616881858	Real period
R	1.8567788824107	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9248g1 18496k2 83232r1 9248f1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 9248g1

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	-4	0	0	-6	+	0	0	-4	0	-12	-8	0	0	-14	0	-12	0	0	-16	0	0	-10	8

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Quadratic twists for elliptic curve 9248g1

-4	8	-3	17
9248g1	18496k2	83232r1	9248f1

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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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