Cremona's table of elliptic curves

58 = 2 · 29

Field	Data	Notes
Atkin-Lehner	2- 29+	Signs for the Atkin-Lehner involutions
Class	58b	Isogeny class
Conductor	58	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	4	Modular degree for the optimal curve
Δ	-29696 = -1 · 210 · 29	Discriminant
Eigenvalues	2- -1  1 -2 -3 -1  8  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,5,9]	[a1,a2,a3,a4,a6]
j	13651919/29696	j-invariant
L	1.0332075093651	L(r)(E,1)/r!
Ω	2.5830187734128	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	464c1 1856a1 522f1 1450a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 58b1

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
-	-1	1	-2	-3	-1	8	0	4	+	-3	8	2	-11	13	-11	0	-8	-12	2	4	15	4	-10	-2

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Quadratic twists for elliptic curve 58b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
464c1	1856a1	522f1	1450a1	2842e1	7018b1	9802a1	16762i1	20938e1	30682g1	1682a1	55738v1	79402d1	97498k1	107242a1	128122j1

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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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