Cremona's table of elliptic curves

9555 = 3 · 5 · 7² · 13

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	9555q	Isogeny class
Conductor	9555	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	-790408262109375 = -1 · 33 · 58 · 78 · 13	Discriminant
Eigenvalues	-1 3- 5+ 7-  4 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,7349,-1330120]	[a1,a2,a3,a4,a6]
Generators	[529:12010:1]	Generators of the group modulo torsion
j	373092501599/6718359375	j-invariant
L	3.2755389909555	L(r)(E,1)/r!
Ω	0.24530319181393	Real period
R	4.4510074338809	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	28665bp1 47775p1 1365b1 124215cw1	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 9555q1

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

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Quadratic twists for elliptic curve 9555q1

-3	5	-7	13
28665bp1	47775p1	1365b1	124215cw1

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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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