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	590a	Isogeny class
Conductor	590	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-115234375000 = -1 · 23 · 512 · 59	Discriminant
Eigenvalues	2+ -2 5+  5 -3 -1  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1909,-36168]	[a1,a2,a3,a4,a6]
j	-768801863379529/115234375000	j-invariant
L	0.71638232572502	L(r)(E,1)/r!
Ω	0.35819116286251	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	4720b2 18880e2 5310q2 2950p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 590a2

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	+	5	-3	-1	3	-4	0	0	8	11	-3	-1	6	12	-	2	-4	-3	2	-1	-3	6	2

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Quadratic twists for elliptic curve 590a2

-4	8	-3	5	-7	-11	13	-59
4720b2	18880e2	5310q2	2950p2	28910o2	71390m2	99710bb2	34810l2

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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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