Cremona's table of elliptic curves

8554 = 2 · 7 · 13 · 47

Field	Data	Notes
Atkin-Lehner	2+ 7+ 13- 47-	Signs for the Atkin-Lehner involutions
Class	8554d	Isogeny class
Conductor	8554	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	44352	Modular degree for the optimal curve
Δ	340083030769664 = 214 · 7 · 134 · 473	Discriminant
Eigenvalues	2+ -2 -2 7+  2 13- -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-22352,929310]	[a1,a2,a3,a4,a6]
Generators	[4:914:1]	Generators of the group modulo torsion
j	1234937412568202617/340083030769664	j-invariant
L	1.653543935891	L(r)(E,1)/r!
Ω	0.50380866087232	Real period
R	0.5470145263177	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	68432u1 76986z1 59878e1 111202y1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 8554d1

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	-2	+	2	-	-2	8	-4	-8	0	-2	-10	10	-	-6	-6	8	-2	-8	6	8	14	-18	2

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Quadratic twists for elliptic curve 8554d1

-4	-3	-7	13
68432u1	76986z1	59878e1	111202y1

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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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