Cremona's table of elliptic curves

17340 = 2² · 3 · 5 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 17+	Signs for the Atkin-Lehner involutions
Class	17340g	Isogeny class
Conductor	17340	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-711527258982000 = -1 · 24 · 3 · 53 · 179	Discriminant
Eigenvalues	2- 3+ 5-  1  3 -4 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,15510,-1051275]	[a1,a2,a3,a4,a6]
Generators	[227:3757:1]	Generators of the group modulo torsion
j	1068359936/1842375	j-invariant
L	4.6357782066216	L(r)(E,1)/r!
Ω	0.26688751454059	Real period
R	2.894963829363	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	69360dr2 52020s2 86700bi2 1020e2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 17340g2

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
-	+	-	1	3	-4	+	-7	0	-3	4	7	-3	8	3	-3	-6	4	-10	0	-11	10	0	18	-2

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Quadratic twists for elliptic curve 17340g2

-4	-3	5	17
69360dr2	52020s2	86700bi2	1020e2

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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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