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
Δ	85820959488 = 28 · 3 · 112 · 314	Discriminant
Eigenvalues	2- 3+  2  2 11+ -2 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-14776332,-21857487288]	[a1,a2,a3,a4,a6]
j	1393746203803968446127568/335238123	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	16368y2 65472bb2 12276c2 102300r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4092a2

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 4092a2

-4	8	-3	5	-11	-31
16368y2	65472bb2	12276c2	102300r2	45012a2	126852l2

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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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