Cremona's table of elliptic curves

20691 = 3² · 11² · 19

Field	Data	Notes
Atkin-Lehner	3- 11- 19-	Signs for the Atkin-Lehner involutions
Class	20691p	Isogeny class
Conductor	20691	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	26880	Modular degree for the optimal curve
Δ	-809750416563 = -1 · 37 · 117 · 19	Discriminant
Eigenvalues	0 3- -4 -2 11- -1 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1452,-48249]	[a1,a2,a3,a4,a6]
Generators	[77:544:1] [143:1633:1]	Generators of the group modulo torsion
j	-262144/627	j-invariant
L	4.8252153362704	L(r)(E,1)/r!
Ω	0.36083856181621	Real period
R	0.83576421821155	Regulator
r	2	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6897e1 1881c1	Quadratic twists by: -3 -11

Hecke Eigenvalues for elliptic curve 20691p1

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
0	-	-4	-2	-	-1	-3	-	-2	-4	-4	2	6	4	-6	-1	-11	-10	-6	3	0	11	-13	9	-6

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Quadratic twists for elliptic curve 20691p1

-3	-11
6897e1	1881c1

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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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