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	24	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-177005728944 = -1 · 24 · 32 · 113 · 314	Discriminant
Eigenvalues	2- 3+  2  2 11+ -6  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-517,-20570]	[a1,a2,a3,a4,a6]
Generators	[65:465:1]	Generators of the group modulo torsion
j	-957007003648/11062858059	j-invariant
L	3.6142233034334	L(r)(E,1)/r!
Ω	0.43197674886906	Real period
R	1.394451326719	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	16368x1 65472bg1 12276f1 102300u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4092c1

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 4092c1

-4	8	-3	5	-11	-31
16368x1	65472bg1	12276f1	102300u1	45012e1	126852m1

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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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