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	2	Product of Tamagawa factors cp
Δ	-5485958875840512 = -1 · 218 · 3 · 178	Discriminant
Eigenvalues	2+ 3-  0 -1  0 -1 17- -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-68066,-7713868]	[a1,a2,a3,a4,a6]
Generators	[545305:35678901:125]	Generators of the group modulo torsion
j	-4999353625/786432	j-invariant
L	2.4952775127127	L(r)(E,1)/r!
Ω	0.14651931503859	Real period
R	8.5151828346164	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13872z2 55488p2 5202m2 43350cj2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734h2

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 1734h2

-4	8	-3	5	-7	17
13872z2	55488p2	5202m2	43350cj2	84966bg2	1734a2

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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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