Cremona's table of elliptic curves

1054 = 2 · 17 · 31

Field	Data	Notes
Atkin-Lehner	2- 17+ 31-	Signs for the Atkin-Lehner involutions
Class	1054a	Isogeny class
Conductor	1054	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-539648 = -1 · 210 · 17 · 31	Discriminant
Eigenvalues	2-  0  0 -4 -4  4 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,0,35]	[a1,a2,a3,a4,a6]
Generators	[1:5:1]	Generators of the group modulo torsion
j	3375/539648	j-invariant
L	3.1921574658681	L(r)(E,1)/r!
Ω	2.315153685659	Real period
R	0.55152407127728	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	8432g1 33728b1 9486b1 26350d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1054a1

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	0	-4	-4	4	+	4	-8	-10	-	2	-2	-6	-8	12	12	14	-8	-12	10	-8	6	-14	-2

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Quadratic twists for elliptic curve 1054a1

-4	8	-3	5	-7	-11	17	-31
8432g1	33728b1	9486b1	26350d1	51646bb1	127534g1	17918b1	32674b1

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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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