Cremona's table of elliptic curves

58176 = 2⁶ · 3² · 101

Field	Data	Notes
Atkin-Lehner	2+ 3- 101-	Signs for the Atkin-Lehner involutions
Class	58176x	Isogeny class
Conductor	58176	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	245760	Modular degree for the optimal curve
Δ	110752642842624 = 214 · 38 · 1013	Discriminant
Eigenvalues	2+ 3-  1  0 -2 -1  7 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-388272,-93120608]	[a1,a2,a3,a4,a6]
Generators	[-2475301:8181:6859]	Generators of the group modulo torsion
j	541981500384256/9272709	j-invariant
L	6.4416577566676	L(r)(E,1)/r!
Ω	0.19125640240778	Real period
R	5.6134571840669	Regulator
r	1	Rank of the group of rational points
S	1.0000000000154	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	58176cf1 7272a1 19392m1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 58176x1

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	0	-2	-1	7	-5	-1	-6	5	6	6	-4	-3	4	-2	2	10	-5	4	-11	2	12	14

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Quadratic twists for elliptic curve 58176x1

-4	8	-3
58176cf1	7272a1	19392m1

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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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