Cremona's table of elliptic curves

1577 = 19 · 83

Field	Data	Notes
Atkin-Lehner	19- 83+	Signs for the Atkin-Lehner involutions
Class	1577a	Isogeny class
Conductor	1577	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-47251651 = -1 · 193 · 832	Discriminant
Eigenvalues	2  2  1  3  3 -6  5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,30,-335]	[a1,a2,a3,a4,a6]
j	2887553024/47251651	j-invariant
L	5.8972767755104	L(r)(E,1)/r!
Ω	0.98287946258506	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25232i1 100928d1 14193c1 39425c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1577a1

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
2	2	1	3	3	-6	5	-	8	-4	-10	-2	4	1	3	12	8	-1	-8	-4	-9	-16	+	0	-8

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Quadratic twists for elliptic curve 1577a1

-4	8	-3	5	-7	-19
25232i1	100928d1	14193c1	39425c1	77273b1	29963d1

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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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