Cremona's table of elliptic curves

59488 = 2⁵ · 11 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	59488h	Isogeny class
Conductor	59488	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	731136	Modular degree for the optimal curve
Δ	-6211352208748544 = -1 · 212 · 11 · 1310	Discriminant
Eigenvalues	2+ -3 -1 -4 11+ 13+ -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,41912,-1863056]	[a1,a2,a3,a4,a6]
Generators	[52:676:1]	Generators of the group modulo torsion
j	411830784/314171	j-invariant
L	1.7096649886064	L(r)(E,1)/r!
Ω	0.23676449217954	Real period
R	1.8052379530421	Regulator
r	1	Rank of the group of rational points
S	0.99999999985106	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59488y1 118976bo1 4576g1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 59488h1

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	-1	-4	+	+	-4	-2	9	-8	7	1	10	-10	-4	-14	-3	-4	5	13	-6	10	6	-15	-9

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Quadratic twists for elliptic curve 59488h1

-4	8	13
59488y1	118976bo1	4576g1

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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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