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	1071a	Isogeny class
Conductor	1071	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4352	Modular degree for the optimal curve
Δ	-3842642130181659 = -1 · 323 · 74 · 17	Discriminant
Eigenvalues	0 3- -1 7+ -3  3 17+  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,32082,-2000768]	[a1,a2,a3,a4,a6]
j	5009339741732864/5271114033171	j-invariant
L	0.95671134122029	L(r)(E,1)/r!
Ω	0.23917783530507	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	17136bj1 68544z1 357a1 26775bn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1071a1

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	+	-3	3	+	3	-7	6	10	4	9	9	-6	10	2	0	-12	12	6	10	-10	4	8

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Quadratic twists for elliptic curve 1071a1

-4	8	-3	5	-7	-11	17
17136bj1	68544z1	357a1	26775bn1	7497k1	129591u1	18207d1

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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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