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	97344fh	Isogeny class
Conductor	97344	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	87687319723720704 = 214 · 38 · 138	Discriminant
Eigenvalues	2- 3- -2  0  0 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-318396,-67667600]	[a1,a2,a3,a4,a6]
Generators	[2237:102051:1]	Generators of the group modulo torsion
j	61918288/1521	j-invariant
L	5.4344269213077	L(r)(E,1)/r!
Ω	0.20128339242178	Real period
R	6.7497209468536	Regulator
r	1	Rank of the group of rational points
S	1.0000000001795	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	97344by2 24336f2 32448da2 7488br2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344fh2

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	0	0	+	-2	4	0	6	0	-2	6	-12	4	6	-8	2	-4	12	14	0	8	-18	6

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Quadratic twists for elliptic curve 97344fh2

-4	8	-3	13
97344by2	24336f2	32448da2	7488br2

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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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