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	1734h	Isogeny class
Conductor	1734	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	3672	Modular degree for the optimal curve
Δ	-12054108858048 = -1 · 26 · 33 · 178	Discriminant
Eigenvalues	2+ 3-  0 -1  0 -1 17- -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,5629,38846]	[a1,a2,a3,a4,a6]
Generators	[39:544:1]	Generators of the group modulo torsion
j	2828375/1728	j-invariant
L	2.4952775127127	L(r)(E,1)/r!
Ω	0.43955794511577	Real period
R	2.8383942782055	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	13872z1 55488p1 5202m1 43350cj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734h1

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
+	-	0	-1	0	-1	-	-7	-6	0	5	5	-12	11	-6	-12	6	5	-7	-12	2	8	-6	0	-7

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Quadratic twists for elliptic curve 1734h1

-4	8	-3	5	-7	17
13872z1	55488p1	5202m1	43350cj1	84966bg1	1734a1

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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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