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	17340a	Isogeny class
Conductor	17340	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-6632550000 = -1 · 24 · 33 · 55 · 173	Discriminant
Eigenvalues	2- 3+ 5+ -3  3 -2 17+ -3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-946,-11555]	[a1,a2,a3,a4,a6]
j	-1192310528/84375	j-invariant
L	0.85727857950552	L(r)(E,1)/r!
Ω	0.42863928975276	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69360de1 52020bh1 86700bl1 17340q1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 17340a1

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
-	+	+	-3	3	-2	+	-3	8	1	-8	-5	-3	4	7	1	0	0	-14	-12	1	2	16	8	10

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Quadratic twists for elliptic curve 17340a1

-4	-3	5	17
69360de1	52020bh1	86700bl1	17340q1

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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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