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	17340d	Isogeny class
Conductor	17340	Conductor
∏ cp	112	Product of Tamagawa factors cp
Δ	-7.1512413391252E+25	Discriminant
Eigenvalues	2- 3+ 5-  0  2  2 17+  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-117830020,638709572632]	[a1,a2,a3,a4,a6]
Generators	[-598:6437475:8]	Generators of the group modulo torsion
j	-29279123829148431184/11573052978515625	j-invariant
L	4.9377490102955	L(r)(E,1)/r!
Ω	0.057766450889808	Real period
R	3.0527784937925	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69360dn2 52020p2 86700bc2 1020f2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 17340d2

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

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Quadratic twists for elliptic curve 17340d2

-4	-3	5	17
69360dn2	52020p2	86700bc2	1020f2

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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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