Cremona's table of elliptic curves

18564 = 2² · 3 · 7 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 13+ 17-	Signs for the Atkin-Lehner involutions
Class	18564n	Isogeny class
Conductor	18564	Conductor
∏ cp	21	Product of Tamagawa factors cp
deg	12096	Modular degree for the optimal curve
Δ	15644328336 = 24 · 37 · 7 · 13 · 173	Discriminant
Eigenvalues	2- 3- -1 7-  2 13+ 17-  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1106,12453]	[a1,a2,a3,a4,a6]
Generators	[-11:153:1]	Generators of the group modulo torsion
j	9359695554304/977770521	j-invariant
L	6.193215553892	L(r)(E,1)/r!
Ω	1.2047811787383	Real period
R	0.2447872124668	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	74256bm1 55692y1 129948o1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 18564n1

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	+	-	5	-3	-9	10	-2	-3	-11	-2	-2	-8	-9	4	6	14	-14	-14	6	-8

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Quadratic twists for elliptic curve 18564n1

-4	-3	-7
74256bm1	55692y1	129948o1

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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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