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	97344fn	Isogeny class
Conductor	97344	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	6.6898440441035E+26	Discriminant
Eigenvalues	2- 3- -2  4 -4 13+ -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-227738316,-448653517936]	[a1,a2,a3,a4,a6]
Generators	[-12023410699686813259647360:-158364552479521321824418268:865382866292146159125]	Generators of the group modulo torsion
j	1416134368422073/725251155408	j-invariant
L	6.3605772293223	L(r)(E,1)/r!
Ω	0.0410573822177	Real period
R	38.729802409914	Regulator
r	1	Rank of the group of rational points
S	1.0000000041322	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97344ci3 24336bs3 32448cg3 7488bt3	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344fn3

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	4	-4	+	-2	8	0	6	-4	-2	-10	4	-8	-10	4	2	16	8	-2	-8	12	14	-10

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Quadratic twists for elliptic curve 97344fn3

-4	8	-3	13
97344ci3	24336bs3	32448cg3	7488bt3

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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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