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	97344dn	Isogeny class
Conductor	97344	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-13757750911696896 = -1 · 233 · 36 · 133	Discriminant
Eigenvalues	2+ 3- -3 -3  0 13-  3  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-185484,-31260944]	[a1,a2,a3,a4,a6]
Generators	[31902:5697536:1]	Generators of the group modulo torsion
j	-1680914269/32768	j-invariant
L	4.0598284197885	L(r)(E,1)/r!
Ω	0.11489235410795	Real period
R	4.4169915078927	Regulator
r	1	Rank of the group of rational points
S	1.0000000001122	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	97344go2 3042h2 10816s2 97344dk2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344dn2

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	-3	0	-	3	6	-6	0	0	3	0	-1	3	-6	6	8	12	-15	-6	10	6	-6	-12

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Quadratic twists for elliptic curve 97344dn2

-4	8	-3	13
97344go2	3042h2	10816s2	97344dk2

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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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