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	97344dq	Isogeny class
Conductor	97344	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	89856	Modular degree for the optimal curve
Δ	-1409582685888 = -1 · 26 · 33 · 138	Discriminant
Eigenvalues	2- 3+  0  1  0 13+  0  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,-57122]	[a1,a2,a3,a4,a6]
j	0	j-invariant
L	3.1307937004647	L(r)(E,1)/r!
Ω	0.39134922689572	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	97344b1 24336y1 97344dq2 97344dr1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344dq1

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
-	+	0	1	0	+	0	8	0	0	7	10	0	-13	0	0	0	13	11	0	17	13	0	0	5

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Quadratic twists for elliptic curve 97344dq1

-4	8	-3	13
97344b1	24336y1	97344dq2	97344dr1

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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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