Cremona's table of elliptic curves

9248 = 2⁵ · 17²

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	9248c	Isogeny class
Conductor	9248	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	26261675072 = 26 · 177	Discriminant
Eigenvalues	2+ -2 -2 -2  2  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6454,197280]	[a1,a2,a3,a4,a6]
Generators	[-23:578:1]	Generators of the group modulo torsion
j	19248832/17	j-invariant
L	2.1715642469514	L(r)(E,1)/r!
Ω	1.181719199769	Real period
R	0.9188156743903	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	9248b1 18496o2 83232bm1 544b1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 9248c1

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
+	-2	-2	-2	2	2	+	-4	-2	-2	10	-10	-2	-4	0	6	-4	-2	16	10	6	6	4	6	14

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Quadratic twists for elliptic curve 9248c1

-4	8	-3	17
9248b1	18496o2	83232bm1	544b1

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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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