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	1734l	Isogeny class
Conductor	1734	Conductor
∏ cp	243	Product of Tamagawa factors cp
deg	38556	Modular degree for the optimal curve
Δ	-70299562860135936 = -1 · 29 · 39 · 178	Discriminant
Eigenvalues	2- 3- -3 -4  3  2 17-  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-463562,-122187996]	[a1,a2,a3,a4,a6]
j	-1579268174113/10077696	j-invariant
L	2.4691117635314	L(r)(E,1)/r!
Ω	0.091448583834496	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	13872bb1 55488u1 5202e1 43350q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734l1

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
-	-	-3	-4	3	2	-	8	6	3	-7	8	6	-4	-6	-9	15	14	2	0	-7	-1	12	0	-13

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Quadratic twists for elliptic curve 1734l1

-4	8	-3	5	-7	17
13872bb1	55488u1	5202e1	43350q1	84966dj1	1734j1

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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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