Cremona's table of elliptic curves

97344 = 2⁶ · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	97344fr	Isogeny class
Conductor	97344	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	319488	Modular degree for the optimal curve
Δ	-342528592670784 = -1 · 26 · 38 · 138	Discriminant
Eigenvalues	2- 3-  3  2 -2 13+  3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6591,-913952]	[a1,a2,a3,a4,a6]
Generators	[8767027317472:10695631352472:73087061741]	Generators of the group modulo torsion
j	-832/9	j-invariant
L	9.5612909182056	L(r)(E,1)/r!
Ω	0.22952145250857	Real period
R	20.828752200948	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	97344fs1 48672bw1 32448df1 97344fz1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344fr1

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	2	-2	+	3	-6	6	-5	0	-1	-5	6	6	3	-12	7	10	-10	11	-8	14	-10	-10

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Quadratic twists for elliptic curve 97344fr1

-4	8	-3	13
97344fs1	48672bw1	32448df1	97344fz1

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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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