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	17340h	Isogeny class
Conductor	17340	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	103680	Modular degree for the optimal curve
Δ	-256149813233520 = -1 · 24 · 33 · 5 · 179	Discriminant
Eigenvalues	2- 3+ 5- -5 -3  2 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-24950,-1692855]	[a1,a2,a3,a4,a6]
Generators	[856:24565:1]	Generators of the group modulo torsion
j	-4447738624/663255	j-invariant
L	3.2439785934508	L(r)(E,1)/r!
Ω	0.18838089474554	Real period
R	1.4350263588003	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	69360dv1 52020y1 86700bo1 1020g1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 17340h1

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
-	+	-	-5	-3	2	+	-7	6	3	-2	-11	3	8	-9	9	12	10	8	-12	7	10	-12	-12	-2

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Quadratic twists for elliptic curve 17340h1

-4	-3	5	17
69360dv1	52020y1	86700bo1	1020g1

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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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