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	17424bp	Isogeny class
Conductor	17424	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	92160	Modular degree for the optimal curve
Δ	-3626128518414336 = -1 · 222 · 310 · 114	Discriminant
Eigenvalues	2- 3-  1  4 11-  3  1  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,25773,2420242]	[a1,a2,a3,a4,a6]
j	43307231/82944	j-invariant
L	3.6681400999727	L(r)(E,1)/r!
Ω	0.30567834166439	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	2178e1 69696gd1 5808bc1 17424br1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bp1

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	4	-	3	1	8	-8	9	0	3	-3	8	12	-11	0	-2	-4	0	-6	4	16	-7	-5

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Quadratic twists for elliptic curve 17424bp1

-4	8	-3	-11
2178e1	69696gd1	5808bc1	17424br1

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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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