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	2	Product of Tamagawa factors cp
Δ	-82044596 = -1 · 22 · 295	Discriminant
Eigenvalues	2- -1  1 -2 -3 -1  8  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-455,-3951]	[a1,a2,a3,a4,a6]
j	-10418796526321/82044596	j-invariant
L	1.0332075093651	L(r)(E,1)/r!
Ω	0.51660375468255	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	464c2 1856a2 522f2 1450a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 58b2

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 58b2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
464c2	1856a2	522f2	1450a2	2842e2	7018b2	9802a2	16762i2	20938e2	30682g2	1682a2	55738v2	79402d2	97498k2	107242a2	128122j2

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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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