Cremona's table of elliptic curves

1590 = 2 · 3 · 5 · 53

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 53+	Signs for the Atkin-Lehner involutions
Class	1590a	Isogeny class
Conductor	1590	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	225076838400000 = 224 · 34 · 55 · 53	Discriminant
Eigenvalues	2+ 3+ 5+  0  4 -2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-15738,-244332]	[a1,a2,a3,a4,a6]
Generators	[-93:699:1]	Generators of the group modulo torsion
j	431137155391783849/225076838400000	j-invariant
L	1.7690060100961	L(r)(E,1)/r!
Ω	0.4515127991792	Real period
R	3.9179531860713	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	12720w1 50880bq1 4770bh1 7950bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1590a1

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

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Quadratic twists for elliptic curve 1590a1

-4	8	-3	5	-7	53
12720w1	50880bq1	4770bh1	7950bt1	77910bb1	84270bn1

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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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