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	32	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-119252736 = -1 · 28 · 38 · 71	Discriminant
Eigenvalues	2- 3- -2  0  0 -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-84,576]	[a1,a2,a3,a4,a6]
Generators	[-6:30:1]	Generators of the group modulo torsion
j	-259108432/465831	j-invariant
L	3.0292679218798	L(r)(E,1)/r!
Ω	1.6656881024149	Real period
R	0.90931427002692	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3408a1 13632a1 5112a1 42600a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1704d1

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 1704d1

-4	8	-3	5	-7	-71
3408a1	13632a1	5112a1	42600a1	83496l1	120984i1

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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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