Cremona's table of elliptic curves

9408 = 2⁶ · 3 · 7²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7-	Signs for the Atkin-Lehner involutions
Class	9408q	Isogeny class
Conductor	9408	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	624529833984 = 216 · 34 · 76	Discriminant
Eigenvalues	2+ 3+ -2 7- -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4769,122529]	[a1,a2,a3,a4,a6]
Generators	[-65:392:1] [-16:441:1]	Generators of the group modulo torsion
j	1556068/81	j-invariant
L	4.6728024550836	L(r)(E,1)/r!
Ω	0.90107146676305	Real period
R	2.5929144509875	Regulator
r	2	Rank of the group of rational points
S	0.99999999999972	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	9408cz3 1176i4 28224by3 192c3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9408q4

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	-	-4	-2	-2	-4	-8	-6	-8	-6	6	-4	0	2	4	-2	4	8	-10	-8	-4	6	-2

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Quadratic twists for elliptic curve 9408q4

-4	8	-3	-7
9408cz3	1176i4	28224by3	192c3

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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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