Cremona's table of elliptic curves

58464 = 2⁵ · 3² · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 29-	Signs for the Atkin-Lehner involutions
Class	58464z	Isogeny class
Conductor	58464	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	215040	Modular degree for the optimal curve
Δ	-499194502926336 = -1 · 212 · 36 · 78 · 29	Discriminant
Eigenvalues	2- 3-  1 7+ -1 -7  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,19188,-330048]	[a1,a2,a3,a4,a6]
j	261652787136/167179229	j-invariant
L	1.1998450564293	L(r)(E,1)/r!
Ω	0.29996126397794	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	58464be1 116928dh1 6496b1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 58464z1

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	-7	6	4	-6	-	-5	-8	0	-3	-3	9	6	2	12	10	-4	-3	-18	16	-12

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Quadratic twists for elliptic curve 58464z1

-4	8	-3
58464be1	116928dh1	6496b1

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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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