Cremona's table of elliptic curves

58 = 2 · 29

Field	Data	Notes
Atkin-Lehner	2+ 29+	Signs for the Atkin-Lehner involutions
Class	58a	Isogeny class
Conductor	58	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4	Modular degree for the optimal curve
Δ	-116 = -1 · 22 · 29	Discriminant
Eigenvalues	2+ -3 -3 -2 -1  3 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	-185193/116	j-invariant
L	0.46370416478825	L(r)(E,1)/r!
Ω	5.4655916988864	Real period
R	0.04242030783993	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	464g1 1856f1 522l1 1450f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 58a1

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
+	-3	-3	-2	-1	3	-4	-8	0	+	3	-8	-2	7	11	1	-4	4	-4	-2	-12	-7	0	-6	-6

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Quadratic twists for elliptic curve 58a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
464g1	1856f1	522l1	1450f1	2842c1	7018d1	9802e1	16762d1	20938i1	30682d1	1682g1	55738l1	79402i1	97498d1	107242b1	128122e1

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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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