Cremona's table of elliptic curves

106575 = 3 · 5² · 7² · 29

Field	Data	Notes
Atkin-Lehner	3- 5- 7- 29-	Signs for the Atkin-Lehner involutions
Class	106575cz	Isogeny class
Conductor	106575	Conductor
∏ cp	102	Product of Tamagawa factors cp
deg	1346400	Modular degree for the optimal curve
Δ	-2078803506666796875 = -1 · 317 · 58 · 72 · 292	Discriminant
Eigenvalues	-1 3- 5- 7- -2 -1  4  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,271487,-42961108]	[a1,a2,a3,a4,a6]
Generators	[827:26924:1]	Generators of the group modulo torsion
j	115615114298495/108606877083	j-invariant
L	5.4961806997171	L(r)(E,1)/r!
Ω	0.14286780609144	Real period
R	0.37716071635191	Regulator
r	1	Rank of the group of rational points
S	1.0000000077566	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	106575o1 106575bf1	Quadratic twists by: 5 -7

Hecke Eigenvalues for elliptic curve 106575cz1

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	-	-	-	-2	-1	4	7	4	-	-4	-3	-4	0	4	0	6	-1	13	10	9	-7	0	0	-19

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Quadratic twists for elliptic curve 106575cz1

5	-7
106575o1	106575bf1

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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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