Cremona's table of elliptic curves

2057 = 11² · 17

Field	Data	Notes
Atkin-Lehner	11+ 17+	Signs for the Atkin-Lehner involutions
Class	2057a	Isogeny class
Conductor	2057	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	-6539203 = -1 · 113 · 173	Discriminant
Eigenvalues	0  2  0 -3 11+  6 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,37,76]	[a1,a2,a3,a4,a6]
Generators	[4:16:1]	Generators of the group modulo torsion
j	4096000/4913	j-invariant
L	3.3061331023339	L(r)(E,1)/r!
Ω	1.588008837109	Real period
R	1.040968105805	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32912q1 18513i1 51425c1 100793g1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2057a1

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	2	0	-3	+	6	+	-6	6	-9	4	-2	-9	-6	3	-3	9	-6	-5	-12	-9	0	0	-15	8

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Quadratic twists for elliptic curve 2057a1

-4	-3	5	-7	-11	17
32912q1	18513i1	51425c1	100793g1	2057b1	34969b1

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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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