Cremona's table of elliptic curves

1581 = 3 · 17 · 31

Field	Data	Notes
Atkin-Lehner	3+ 17+ 31+	Signs for the Atkin-Lehner involutions
Class	1581a	Isogeny class
Conductor	1581	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	200	Modular degree for the optimal curve
Δ	-3969891 = -1 · 35 · 17 · 312	Discriminant
Eigenvalues	0 3+  1 -2  1  1 17+  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-125,590]	[a1,a2,a3,a4,a6]
Generators	[10:15:1]	Generators of the group modulo torsion
j	-217732612096/3969891	j-invariant
L	2.1107462540883	L(r)(E,1)/r!
Ω	2.4784627193697	Real period
R	0.42581763235581	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	25296n1 101184l1 4743c1 39525d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1581a1

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	+	1	-2	1	1	+	3	-3	6	+	4	-9	-1	0	-2	-8	6	-4	-16	-4	-12	-4	-12	12

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Quadratic twists for elliptic curve 1581a1

-4	8	-3	5	-7	17	-31
25296n1	101184l1	4743c1	39525d1	77469bd1	26877b1	49011h1

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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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