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	97344x	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	[325:1521:1] [352:612:1]	Generators of the group modulo torsion
j	137842000/117	j-invariant
L	10.992939212715	L(r)(E,1)/r!
Ω	0.41831809818508	Real period
R	3.2848624231398	Regulator
r	2	Rank of the group of rational points
S	0.99999999995775	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97344eh2 12168b2 32448a2 7488v2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344x2

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 97344x2

-4	8	-3	13
97344eh2	12168b2	32448a2	7488v2

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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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