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	9408cf	Isogeny class
Conductor	9408	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-43352064 = -1 · 215 · 33 · 72	Discriminant
Eigenvalues	2- 3+  3 7- -1 -4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-289,2017]	[a1,a2,a3,a4,a6]
Generators	[9:8:1]	Generators of the group modulo torsion
j	-1668296/27	j-invariant
L	4.3376023523494	L(r)(E,1)/r!
Ω	2.0326154355469	Real period
R	0.53350012457993	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9408dc1 4704o1 28224gf1 9408cn1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9408cf1

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
-	+	3	-	-1	-4	-4	0	-8	7	11	-4	4	-2	-2	11	-7	10	10	-6	6	-11	-11	-6	-7

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Quadratic twists for elliptic curve 9408cf1

-4	8	-3	-7
9408dc1	4704o1	28224gf1	9408cn1

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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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