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	97344eh	Isogeny class
Conductor	97344	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	6745178440286208 = 214 · 38 · 137	Discriminant
Eigenvalues	2- 3-  0  0  6 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-415740,-103100816]	[a1,a2,a3,a4,a6]
Generators	[5928:453596:1]	Generators of the group modulo torsion
j	137842000/117	j-invariant
L	7.2938842420662	L(r)(E,1)/r!
Ω	0.18802527448073	Real period
R	4.8490051828043	Regulator
r	1	Rank of the group of rational points
S	0.99999999978396	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97344x2 24336c2 32448cu2 7488bx2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344eh2

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	0	6	+	-2	0	4	-6	-4	-2	0	4	-10	-10	-6	6	12	-2	-6	16	6	4	-14

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Quadratic twists for elliptic curve 97344eh2

-4	8	-3	13
97344x2	24336c2	32448cu2	7488bx2

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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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