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	17424bc	Isogeny class
Conductor	17424	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	92160	Modular degree for the optimal curve
Δ	8827392881590272 = 224 · 33 · 117	Discriminant
Eigenvalues	2- 3+  0  2 11- -2  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-125235,16448498]	[a1,a2,a3,a4,a6]
Generators	[143:1210:1]	Generators of the group modulo torsion
j	1108717875/45056	j-invariant
L	5.5781468537607	L(r)(E,1)/r!
Ω	0.40815556702106	Real period
R	1.7083396946148	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2178a1 69696ee1 17424bd3 1584j1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bc1

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

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Quadratic twists for elliptic curve 17424bc1

-4	8	-3	-11
2178a1	69696ee1	17424bd3	1584j1

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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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