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
deg	20736	Modular degree for the optimal curve
Δ	-886331533680 = -1 · 24 · 33 · 5 · 177	Discriminant
Eigenvalues	2- 3+ 5-  1  3 -4 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1830,55017]	[a1,a2,a3,a4,a6]
Generators	[-28:289:1]	Generators of the group modulo torsion
j	-1755904/2295	j-invariant
L	4.6357782066216	L(r)(E,1)/r!
Ω	0.80066254362176	Real period
R	0.96498794312101	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	69360dr1 52020s1 86700bi1 1020e1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 17340g1

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 17340g1

-4	-3	5	17
69360dr1	52020s1	86700bi1	1020e1

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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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