Cremona's table of elliptic curves

1071 = 3² · 7 · 17

Field	Data	Notes
Atkin-Lehner	3- 7- 17+	Signs for the Atkin-Lehner involutions
Class	1071c	Isogeny class
Conductor	1071	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-89266779 = -1 · 37 · 74 · 17	Discriminant
Eigenvalues	0 3- -1 7-  5 -5 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-48,472]	[a1,a2,a3,a4,a6]
Generators	[10:31:1]	Generators of the group modulo torsion
j	-16777216/122451	j-invariant
L	2.1467633811823	L(r)(E,1)/r!
Ω	1.6407927125207	Real period
R	0.16354620580654	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17136w1 68544bu1 357b1 26775bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1071c1

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	-5	+	-5	1	6	-6	4	-7	-7	-6	-6	-14	0	-12	-4	6	-6	6	-12	8

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Quadratic twists for elliptic curve 1071c1

-4	8	-3	5	-7	-11	17
17136w1	68544bu1	357b1	26775bc1	7497l1	129591m1	18207a1

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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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