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	20592v	Isogeny class
Conductor	20592	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	-3557332905984 = -1 · 212 · 33 · 114 · 133	Discriminant
Eigenvalues	2- 3+  2  2 11- 13+ -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,261,90730]	[a1,a2,a3,a4,a6]
Generators	[23:330:1]	Generators of the group modulo torsion
j	17779581/32166277	j-invariant
L	6.368123283794	L(r)(E,1)/r!
Ω	0.61920053458543	Real period
R	1.2855534935983	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	1287a1 82368cw1 20592q1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 20592v1

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

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Quadratic twists for elliptic curve 20592v1

-4	8	-3
1287a1	82368cw1	20592q1

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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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