Cremona's table of elliptic curves

1704 = 2³ · 3 · 71

Field	Data	Notes
Atkin-Lehner	2- 3- 71+	Signs for the Atkin-Lehner involutions
Class	1704d	Isogeny class
Conductor	1704	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1308672 = 211 · 32 · 71	Discriminant
Eigenvalues	2- 3- -2  0  0 -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-27264,1723680]	[a1,a2,a3,a4,a6]
Generators	[810:855:8]	Generators of the group modulo torsion
j	1094405855968514/639	j-invariant
L	3.0292679218798	L(r)(E,1)/r!
Ω	1.6656881024149	Real period
R	3.6372570801077	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3408a3 13632a4 5112a3 42600a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1704d4

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	0	0	-6	2	4	0	-2	-8	-2	-6	-4	-8	2	8	2	-8	+	-6	-16	12	-6	10

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Quadratic twists for elliptic curve 1704d4

-4	8	-3	5	-7	-71
3408a3	13632a4	5112a3	42600a4	83496l4	120984i4

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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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