Cremona's table of elliptic curves

59584 = 2⁶ · 7² · 19

Field	Data	Notes
Atkin-Lehner	2- 7+ 19-	Signs for the Atkin-Lehner involutions
Class	59584bt	Isogeny class
Conductor	59584	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	322560	Modular degree for the optimal curve
Δ	-29402062718500864 = -1 · 228 · 78 · 19	Discriminant
Eigenvalues	2-  0 -1 7+ -5  2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-39788,8797264]	[a1,a2,a3,a4,a6]
Generators	[-243:2029:1]	Generators of the group modulo torsion
j	-4609521/19456	j-invariant
L	3.9077724985549	L(r)(E,1)/r!
Ω	0.32458478385185	Real period
R	6.0196483213082	Regulator
r	1	Rank of the group of rational points
S	1.0000000000212	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59584a1 14896w1 59584ce1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 59584bt1

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
-	0	-1	+	-5	2	-6	-	5	0	-4	4	4	-11	-3	-4	14	-5	6	-6	1	16	-13	18	-12

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Quadratic twists for elliptic curve 59584bt1

-4	8	-7
59584a1	14896w1	59584ce1

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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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