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	9768i	Isogeny class
Conductor	9768	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	41218771968 = 210 · 35 · 112 · 372	Discriminant
Eigenvalues	2+ 3-  0 -2 11+  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5048,136032]	[a1,a2,a3,a4,a6]
Generators	[28:132:1]	Generators of the group modulo torsion
j	13895296694500/40252707	j-invariant
L	5.0530676090102	L(r)(E,1)/r!
Ω	1.149500340369	Real period
R	0.43958817858099	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	19536e2 78144l2 29304p2 107448y2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 9768i2

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

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Quadratic twists for elliptic curve 9768i2

-4	8	-3	-11
19536e2	78144l2	29304p2	107448y2

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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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