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	17424k	Isogeny class
Conductor	17424	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1320148889655552 = 28 · 37 · 119	Discriminant
Eigenvalues	2+ 3- -2  2 11+  0 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-187671,31243894]	[a1,a2,a3,a4,a6]
j	1661168/3	j-invariant
L	0.96556148322985	L(r)(E,1)/r!
Ω	0.48278074161493	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8712f2 69696fd2 5808h2 17424l2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424k2

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	2	+	0	-6	-6	-4	2	8	2	-10	-10	0	-6	0	-4	4	0	4	10	12	-18	18

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Quadratic twists for elliptic curve 17424k2

-4	8	-3	-11
8712f2	69696fd2	5808h2	17424l2

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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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