Cremona's table of elliptic curves

20592 = 2⁴ · 3² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 13-	Signs for the Atkin-Lehner involutions
Class	20592bk	Isogeny class
Conductor	20592	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	34560	Modular degree for the optimal curve
Δ	-2309192810496 = -1 · 217 · 36 · 11 · 133	Discriminant
Eigenvalues	2- 3- -3  1 11+ 13- -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-939,73946]	[a1,a2,a3,a4,a6]
Generators	[-38:234:1] [-11:288:1]	Generators of the group modulo torsion
j	-30664297/773344	j-invariant
L	6.6601982689207	L(r)(E,1)/r!
Ω	0.68607038157734	Real period
R	0.40448949358083	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2574y1 82368er1 2288l1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 20592bk1

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	1	+	-	-6	-8	-3	-9	-2	-10	-9	1	0	-6	-3	-7	7	12	-1	4	0	-12	-4

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Quadratic twists for elliptic curve 20592bk1

-4	8	-3
2574y1	82368er1	2288l1

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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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