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	4092c	Isogeny class
Conductor	4092	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	1307497052928 = 28 · 3 · 116 · 312	Discriminant
Eigenvalues	2- 3+  2  2 11+ -6  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-14932,-695192]	[a1,a2,a3,a4,a6]
Generators	[158:930:1]	Generators of the group modulo torsion
j	1438357277593168/5107410363	j-invariant
L	3.6142233034334	L(r)(E,1)/r!
Ω	0.43197674886906	Real period
R	2.7889026534381	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16368x2 65472bg2 12276f2 102300u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4092c2

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	+	-6	4	-2	0	-8	-	2	-12	6	-8	-2	-12	6	-12	-8	2	-10	8	18	14

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Quadratic twists for elliptic curve 4092c2

-4	8	-3	5	-11	-31
16368x2	65472bg2	12276f2	102300u2	45012e2	126852m2

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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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