Cremona's table of elliptic curves

4092 = 2² · 3 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+ 31+	Signs for the Atkin-Lehner involutions
Class	4092a	Isogeny class
Conductor	4092	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	36480	Modular degree for the optimal curve
Δ	-1350979403306544 = -1 · 24 · 32 · 11 · 318	Discriminant
Eigenvalues	2- 3+  2  2 11+ -2 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-923517,-341295030]	[a1,a2,a3,a4,a6]
j	-5444260314792559771648/84436212706659	j-invariant
L	1.9250760936004	L(r)(E,1)/r!
Ω	0.077003043744018	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	25	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16368y1 65472bb1 12276c1 102300r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4092a1

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

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Quadratic twists for elliptic curve 4092a1

-4	8	-3	5	-11	-31
16368y1	65472bb1	12276c1	102300r1	45012a1	126852l1

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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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