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	1071b	Isogeny class
Conductor	1071	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-526491819 = -1 · 37 · 72 · 173	Discriminant
Eigenvalues	-2 3- -1 7+ -1  1 17-  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,177,630]	[a1,a2,a3,a4,a6]
Generators	[65:535:1]	Generators of the group modulo torsion
j	841232384/722211	j-invariant
L	1.2707447389281	L(r)(E,1)/r!
Ω	1.0696200351861	Real period
R	0.049501407708884	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	17136bn1 68544bj1 357c1 26775bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1071b1

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
-2	-	-1	+	-1	1	-	1	3	2	0	-6	1	5	-12	0	0	-2	-8	0	6	-4	-6	-16	-12

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Quadratic twists for elliptic curve 1071b1

-4	8	-3	5	-7	-11	17
17136bn1	68544bj1	357c1	26775bl1	7497j1	129591t1	18207g1

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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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