Cremona's table of elliptic curves

2057 = 11² · 17

Field	Data	Notes
Atkin-Lehner	11- 17+	Signs for the Atkin-Lehner involutions
Class	2057c	Isogeny class
Conductor	2057	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-147962546281 = -1 · 116 · 174	Discriminant
Eigenvalues	1  0 -2 -4 11-  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-83,18530]	[a1,a2,a3,a4,a6]
j	-35937/83521	j-invariant
L	0.827871493355	L(r)(E,1)/r!
Ω	0.827871493355	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32912t3 18513q4 51425u3 100793m3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2057c4

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
1	0	-2	-4	-	2	+	4	4	-6	4	-2	6	-4	0	6	-12	10	4	-4	6	-12	4	10	2

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Quadratic twists for elliptic curve 2057c4

-4	-3	5	-7	-11	17
32912t3	18513q4	51425u3	100793m3	17a1	34969e3

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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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