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	17424bx	Isogeny class
Conductor	17424	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	115200	Modular degree for the optimal curve
Δ	-13421741009860656 = -1 · 24 · 316 · 117	Discriminant
Eigenvalues	2- 3- -2  2 11- -6 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-84216,-10934165]	[a1,a2,a3,a4,a6]
j	-3196715008/649539	j-invariant
L	0.55444664673068	L(r)(E,1)/r!
Ω	0.13861166168267	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	4356g1 69696gi1 5808be1 1584m1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bx1

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	-	-6	-4	-2	-8	0	0	-6	0	10	0	-14	-12	14	-4	0	-6	2	-16	14	-2

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Quadratic twists for elliptic curve 17424bx1

-4	8	-3	-11
4356g1	69696gi1	5808be1	1584m1

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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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