Cremona's table of elliptic curves

1734 = 2 · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17-	Signs for the Atkin-Lehner involutions
Class	1734d	Isogeny class
Conductor	1734	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	4284	Modular degree for the optimal curve
Δ	-2678690857344 = -1 · 27 · 3 · 178	Discriminant
Eigenvalues	2+ 3+ -1  4 -3  6 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,717,-78099]	[a1,a2,a3,a4,a6]
j	5831/384	j-invariant
L	1.1575250643027	L(r)(E,1)/r!
Ω	0.38584168810091	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	13872bp1 55488bx1 5202n1 43350dj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734d1

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
+	+	-1	4	-3	6	-	4	6	-7	-3	8	2	-4	-2	13	9	-10	-6	-12	-7	-5	12	4	3

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Quadratic twists for elliptic curve 1734d1

-4	8	-3	5	-7	17
13872bp1	55488bx1	5202n1	43350dj1	84966cl1	1734e1

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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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