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	9768a	Isogeny class
Conductor	9768	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	381655296 = 28 · 32 · 112 · 372	Discriminant
Eigenvalues	2+ 3+  2  0 11+  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-412,3220]	[a1,a2,a3,a4,a6]
j	30285104848/1490841	j-invariant
L	1.6712590350213	L(r)(E,1)/r!
Ω	1.6712590350213	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	19536n2 78144bl2 29304r2 107448o2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 9768a2

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

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Quadratic twists for elliptic curve 9768a2

-4	8	-3	-11
19536n2	78144bl2	29304r2	107448o2

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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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