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	17424cd	Isogeny class
Conductor	17424	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	354816	Modular degree for the optimal curve
Δ	-3528757982049290496 = -1 · 28 · 312 · 1110	Discriminant
Eigenvalues	2- 3- -3  2 11- -5 -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-570999,189073874]	[a1,a2,a3,a4,a6]
j	-4253392/729	j-invariant
L	0.48126779922347	L(r)(E,1)/r!
Ω	0.24063389961173	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	4356j1 69696gr1 5808t1 17424ce1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424cd1

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
-	-	-3	2	-	-5	-3	-4	6	-9	-8	-7	-3	-10	12	9	-6	-14	-2	-6	10	8	0	3	-1

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Quadratic twists for elliptic curve 17424cd1

-4	8	-3	-11
4356j1	69696gr1	5808t1	17424ce1

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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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