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	17424bw	Isogeny class
Conductor	17424	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	2091115841214394368 = 212 · 39 · 1110	Discriminant
Eigenvalues	2- 3-  2  4 11-  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2552979,-1568527598]	[a1,a2,a3,a4,a6]
j	347873904937/395307	j-invariant
L	3.8222347306038	L(r)(E,1)/r!
Ω	0.11944483533137	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1089g3 69696gp4 5808bg3 1584q3	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bw3

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
-	-	2	4	-	2	-2	0	8	-6	8	6	-2	0	8	-6	-4	-6	4	0	14	-4	-12	6	2

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Quadratic twists for elliptic curve 17424bw3

-4	8	-3	-11
1089g3	69696gp4	5808bg3	1584q3

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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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