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	1734g	Isogeny class
Conductor	1734	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	14772192228 = 22 · 32 · 177	Discriminant
Eigenvalues	2+ 3-  4  2  0 -6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-729,4744]	[a1,a2,a3,a4,a6]
j	1771561/612	j-invariant
L	2.2933508150586	L(r)(E,1)/r!
Ω	1.1466754075293	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13872y1 55488o1 5202l1 43350cd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734g1

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
+	-	4	2	0	-6	+	4	-6	4	6	4	10	-4	4	-2	12	4	-12	6	-2	-10	-12	-2	-6

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Quadratic twists for elliptic curve 1734g1

-4	8	-3	5	-7	17
13872y1	55488o1	5202l1	43350cd1	84966bf1	102a1

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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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