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	6	Product of Tamagawa factors cp
deg	352	Modular degree for the optimal curve
Δ	-256723750 = -1 · 2 · 54 · 593	Discriminant
Eigenvalues	2+ -2 5+  5 -3 -1  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,156,176]	[a1,a2,a3,a4,a6]
j	423733973831/256723750	j-invariant
L	0.71638232572502	L(r)(E,1)/r!
Ω	1.0745734885875	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	4720b1 18880e1 5310q1 2950p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 590a1

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 590a1

-4	8	-3	5	-7	-11	13	-59
4720b1	18880e1	5310q1	2950p1	28910o1	71390m1	99710bb1	34810l1

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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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