Cremona's table of elliptic curves

2057 = 11² · 17

Field	Data	Notes
Atkin-Lehner	11- 17+	Signs for the Atkin-Lehner involutions
Class	2057d	Isogeny class
Conductor	2057	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3600	Modular degree for the optimal curve
Δ	-40085110747 = -1 · 119 · 17	Discriminant
Eigenvalues	-2  0  4  5 11- -4 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,847,-1664]	[a1,a2,a3,a4,a6]
j	37933056/22627	j-invariant
L	1.3403801514456	L(r)(E,1)/r!
Ω	0.67019007572282	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32912v1 18513t1 51425w1 100793o1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2057d1

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	0	4	5	-	-4	+	-2	-2	3	4	-2	3	2	3	9	-3	10	7	2	3	0	-14	1	-10

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Quadratic twists for elliptic curve 2057d1

-4	-3	5	-7	-11	17
32912v1	18513t1	51425w1	100793o1	187b1	34969j1

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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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