Cremona's table of elliptic curves

590 = 2 · 5 · 59

Field	Data	Notes
Atkin-Lehner	2+ 5- 59-	Signs for the Atkin-Lehner involutions
Class	590c	Isogeny class
Conductor	590	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-11800 = -1 · 23 · 52 · 59	Discriminant
Eigenvalues	2+  0 5-  1 -5 -7  1 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,1,5]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	59319/11800	j-invariant
L	1.6137866011813	L(r)(E,1)/r!
Ω	3.1049556815083	Real period
R	0.25987272713622	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	4720d1 18880a1 5310l1 2950o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 590c1

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	-5	-7	1	-2	4	6	-10	-7	-7	7	-4	12	-	-6	12	-13	-10	5	17	0	-12

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Quadratic twists for elliptic curve 590c1

-4	8	-3	5	-7	-11	13	-59
4720d1	18880a1	5310l1	2950o1	28910c1	71390p1	99710r1	34810m1

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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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