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	9408bz	Isogeny class
Conductor	9408	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	474360768 = 26 · 32 · 77	Discriminant
Eigenvalues	2- 3+  2 7-  0  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4132,-100862]	[a1,a2,a3,a4,a6]
Generators	[1563:61720:1]	Generators of the group modulo torsion
j	1036433728/63	j-invariant
L	4.3930755956833	L(r)(E,1)/r!
Ω	0.59545960095245	Real period
R	7.3776215693836	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9408cu1 4704be2 28224fy1 1344q1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9408bz1

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	-	0	2	-2	4	0	-6	0	-6	6	-8	-8	-6	-12	10	-16	-8	6	8	-12	14	6

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Quadratic twists for elliptic curve 9408bz1

-4	8	-3	-7
9408cu1	4704be2	28224fy1	1344q1

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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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