Cremona's table of elliptic curves

9768 = 2³ · 3 · 11 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 37-	Signs for the Atkin-Lehner involutions
Class	9768g	Isogeny class
Conductor	9768	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-17940495817728 = -1 · 210 · 316 · 11 · 37	Discriminant
Eigenvalues	2+ 3+ -2  0 11-  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,6496,-32580]	[a1,a2,a3,a4,a6]
Generators	[8430:114065:216]	Generators of the group modulo torsion
j	29600220537212/17520015447	j-invariant
L	3.3176276611301	L(r)(E,1)/r!
Ω	0.40424474207867	Real period
R	8.2069778918347	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	19536l4 78144w3 29304i3 107448s3	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 9768g4

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

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Quadratic twists for elliptic curve 9768g4

-4	8	-3	-11
19536l4	78144w3	29304i3	107448s3

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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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