Cremona's table of elliptic curves

9933 = 3 · 7 · 11 · 43

Field	Data	Notes
Atkin-Lehner	3+ 7+ 11+ 43-	Signs for the Atkin-Lehner involutions
Class	9933a	Isogeny class
Conductor	9933	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	8703095910201 = 38 · 72 · 114 · 432	Discriminant
Eigenvalues	-1 3+  2 7+ 11+ -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-8432,258536]	[a1,a2,a3,a4,a6]
j	66300793297143553/8703095910201	j-invariant
L	0.70632653342118	L(r)(E,1)/r!
Ω	0.70632653342118	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	29799g2 69531l2 109263k2	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 9933a2

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
-1	+	2	+	+	-2	2	4	-8	-2	-4	-2	-6	-	12	-10	8	10	-4	0	-2	-8	16	6	2

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Quadratic twists for elliptic curve 9933a2

-3	-7	-11
29799g2	69531l2	109263k2

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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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