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	97344by	Isogeny class
Conductor	97344	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	8993571253714944 = 216 · 37 · 137	Discriminant
Eigenvalues	2+ 3- -2  0  0 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5063916,4386090800]	[a1,a2,a3,a4,a6]
j	62275269892/39	j-invariant
L	1.3577349520038	L(r)(E,1)/r!
Ω	0.33943375281473	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97344fh4 12168n3 32448c4 7488n3	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344by4

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 97344by4

-4	8	-3	13
97344fh4	12168n3	32448c4	7488n3

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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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