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	4092b	Isogeny class
Conductor	4092	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-4861296 = -1 · 24 · 34 · 112 · 31	Discriminant
Eigenvalues	2- 3+ -3 -3 11+ -2 -4 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-22,121]	[a1,a2,a3,a4,a6]
Generators	[-5:9:1] [0:11:1]	Generators of the group modulo torsion
j	-76995328/303831	j-invariant
L	3.3596284775237	L(r)(E,1)/r!
Ω	2.1245377935109	Real period
R	0.13177879943999	Regulator
r	2	Rank of the group of rational points
S	0.99999999999958	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16368bc1 65472be1 12276d1 102300s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4092b1

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
-	+	-3	-3	+	-2	-4	-7	-2	-10	+	0	-7	2	0	-2	9	10	-16	-15	-6	-10	0	-18	-7

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Quadratic twists for elliptic curve 4092b1

-4	8	-3	5	-11	-31
16368bc1	65472be1	12276d1	102300s1	45012b1	126852o1

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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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