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	9408r	Isogeny class
Conductor	9408	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-17709468672 = -1 · 210 · 3 · 78	Discriminant
Eigenvalues	2+ 3+  4 7- -2 -6  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-261,6693]	[a1,a2,a3,a4,a6]
j	-16384/147	j-invariant
L	2.1015249640723	L(r)(E,1)/r!
Ω	1.0507624820361	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9408dd1 588f1 28224cu1 1344i1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9408r1

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

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Quadratic twists for elliptic curve 9408r1

-4	8	-3	-7
9408dd1	588f1	28224cu1	1344i1

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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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