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	20	Product of Tamagawa factors cp
Δ	8887328 = 25 · 172 · 312	Discriminant
Eigenvalues	2-  0  0 -4 -4  4 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-160,803]	[a1,a2,a3,a4,a6]
Generators	[-1:31:1]	Generators of the group modulo torsion
j	450335804625/8887328	j-invariant
L	3.1921574658681	L(r)(E,1)/r!
Ω	2.315153685659	Real period
R	0.27576203563864	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	8432g2 33728b2 9486b2 26350d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1054a2

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 1054a2

-4	8	-3	5	-7	-11	17	-31
8432g2	33728b2	9486b2	26350d2	51646bb2	127534g2	17918b2	32674b2

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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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