Cremona's table of elliptic curves

1534 = 2 · 13 · 59

Field	Data	Notes
Atkin-Lehner	2+ 13+ 59+	Signs for the Atkin-Lehner involutions
Class	1534a	Isogeny class
Conductor	1534	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1176	Modular degree for the optimal curve
Δ	-978912896 = -1 · 27 · 133 · 592	Discriminant
Eigenvalues	2+ -1 -3  5 -2 13+  1  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,206,1076]	[a1,a2,a3,a4,a6]
Generators	[-1:30:1]	Generators of the group modulo torsion
j	959460498647/978912896	j-invariant
L	1.6651774653208	L(r)(E,1)/r!
Ω	1.0325699107317	Real period
R	0.80632674263227	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	12272h1 49088i1 13806i1 38350v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1534a1

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	-3	5	-2	+	1	6	-6	8	-8	3	-8	-9	3	4	+	6	4	-5	-12	-12	-2	-2	-6

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Quadratic twists for elliptic curve 1534a1

-4	8	-3	5	-7	13	-59
12272h1	49088i1	13806i1	38350v1	75166j1	19942k1	90506f1

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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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