Cremona's table of elliptic curves

17424 = 2⁴ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3- 11-	Signs for the Atkin-Lehner involutions
Class	17424r	Isogeny class
Conductor	17424	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-592628990976 = -1 · 210 · 314 · 112	Discriminant
Eigenvalues	2+ 3-  1  0 11-  1  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2013,-12782]	[a1,a2,a3,a4,a6]
Generators	[59:558:1]	Generators of the group modulo torsion
j	9987164/6561	j-invariant
L	5.5990825166706	L(r)(E,1)/r!
Ω	0.52307897911297	Real period
R	2.6760215666502	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	8712i1 69696ga1 5808l1 17424s1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424r1

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	0	-	1	3	0	4	-1	0	-1	-9	4	-4	-3	12	-14	-16	-12	-10	4	0	5	-5

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Quadratic twists for elliptic curve 17424r1

-4	8	-3	-11
8712i1	69696ga1	5808l1	17424s1

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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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