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	1734f	Isogeny class
Conductor	1734	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	307379775880224 = 25 · 34 · 179	Discriminant
Eigenvalues	2+ 3- -2 -2  0 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-839407,295939010]	[a1,a2,a3,a4,a6]
j	551569744601/2592	j-invariant
L	0.96274493715361	L(r)(E,1)/r!
Ω	0.4813724685768	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	13872w2 55488i2 5202j2 43350ca2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734f2

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
+	-	-2	-2	0	-6	+	0	6	6	10	2	0	-4	8	6	0	10	8	10	-16	-6	16	10	12

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Quadratic twists for elliptic curve 1734f2

-4	8	-3	5	-7	17
13872w2	55488i2	5202j2	43350ca2	84966t2	1734c2

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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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