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
deg	294912	Modular degree for the optimal curve
Δ	10760379282432 = 210 · 314 · 133	Discriminant
Eigenvalues	2- 3- -4  2 -2 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12792,534040]	[a1,a2,a3,a4,a6]
Generators	[113:729:1] [17:567:1]	Generators of the group modulo torsion
j	141150208/6561	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	97344dp1 24336w1 32448do1 97344gq1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344gs1

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 97344gs1

-4	8	-3	13
97344dp1	24336w1	32448do1	97344gq1

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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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