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	36192d	Isogeny class
Conductor	36192	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-5160129122304 = -1 · 212 · 32 · 136 · 29	Discriminant
Eigenvalues	2+ 3+  2 -2  0 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1537,-111215]	[a1,a2,a3,a4,a6]
j	-98099748928/1259797149	j-invariant
L	1.3080047365319	L(r)(E,1)/r!
Ω	0.32700118413268	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	36192m2 72384do1 108576bc2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 36192d2

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

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Quadratic twists for elliptic curve 36192d2

-4	8	-3
36192m2	72384do1	108576bc2

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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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