Cremona's table of elliptic curves

36192 = 2⁵ · 3 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 13- 29+	Signs for the Atkin-Lehner involutions
Class	36192s	Isogeny class
Conductor	36192	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	11264	Modular degree for the optimal curve
Δ	81866304 = 26 · 32 · 132 · 292	Discriminant
Eigenvalues	2+ 3- -2  4  0 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-254,-1584]	[a1,a2,a3,a4,a6]
Generators	[7710:41041:216]	Generators of the group modulo torsion
j	28428476608/1279161	j-invariant
L	7.3263724917311	L(r)(E,1)/r!
Ω	1.1988259091356	Real period
R	6.1112897509971	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	36192j1 72384bw2 108576bo1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 36192s1

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

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Quadratic twists for elliptic curve 36192s1

-4	8	-3
36192j1	72384bw2	108576bo1

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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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