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	1581b	Isogeny class
Conductor	1581	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2499561 = 32 · 172 · 312	Discriminant
Eigenvalues	-1 3+  2  0  4  6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-37,26]	[a1,a2,a3,a4,a6]
j	5611284433/2499561	j-invariant
L	1.156103306659	L(r)(E,1)/r!
Ω	2.312206613318	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	25296m2 101184o2 4743d2 39525f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1581b2

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

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Quadratic twists for elliptic curve 1581b2

-4	8	-3	5	-7	17	-31
25296m2	101184o2	4743d2	39525f2	77469ba2	26877a2	49011i2

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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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