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	97344q	Isogeny class
Conductor	97344	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	172032	Modular degree for the optimal curve
Δ	-27757935968256 = -1 · 214 · 33 · 137	Discriminant
Eigenvalues	2+ 3+ -2 -2 -4 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,6084,175760]	[a1,a2,a3,a4,a6]
Generators	[13:507:1]	Generators of the group modulo torsion
j	11664/13	j-invariant
L	3.0579577574445	L(r)(E,1)/r!
Ω	0.44264775987041	Real period
R	0.8635415239682	Regulator
r	1	Rank of the group of rational points
S	0.99999999618297	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97344dx1 12168l1 97344i1 7488e1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344q1

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

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Quadratic twists for elliptic curve 97344q1

-4	8	-3	13
97344dx1	12168l1	97344i1	7488e1

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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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