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	97344gs	Isogeny class
Conductor	97344	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	2125507018752 = 214 · 310 · 133	Discriminant
Eigenvalues	2- 3- -4  2 -2 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-202332,35030320]	[a1,a2,a3,a4,a6]
Generators	[-508:2592:1] [221:1053:1]	Generators of the group modulo torsion
j	34909201168/81	j-invariant
L	9.1257684040282	L(r)(E,1)/r!
Ω	0.71228562411441	Real period
R	3.2029877114262	Regulator
r	2	Rank of the group of rational points
S	0.99999999997505	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97344dp2 24336w2 32448do2 97344gq2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344gs2

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

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Quadratic twists for elliptic curve 97344gs2

-4	8	-3	13
97344dp2	24336w2	32448do2	97344gq2

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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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