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	97344bk	Isogeny class
Conductor	97344	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	294912	Modular degree for the optimal curve
Δ	-785965262045184 = -1 · 222 · 38 · 134	Discriminant
Eigenvalues	2+ 3- -1 -2  2 13+ -5  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2028,1349296]	[a1,a2,a3,a4,a6]
Generators	[-90:896:1] [38:-1152:1]	Generators of the group modulo torsion
j	-169/144	j-invariant
L	10.430389251116	L(r)(E,1)/r!
Ω	0.40700054767474	Real period
R	3.203432191832	Regulator
r	2	Rank of the group of rational points
S	0.99999999990411	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	97344ex1 3042j1 32448y1 97344bd1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344bk1

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
+	-	-1	-2	2	+	-5	2	-6	-9	-4	11	-5	-10	-2	-1	-8	11	-2	14	-13	-4	6	-2	-2

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Quadratic twists for elliptic curve 97344bk1

-4	8	-3	13
97344ex1	3042j1	32448y1	97344bd1

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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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