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	17424o	Isogeny class
Conductor	17424	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	84480	Modular degree for the optimal curve
Δ	-9721096369281792 = -1 · 28 · 311 · 118	Discriminant
Eigenvalues	2+ 3-  0  1 11-  6 -4  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-79860,-9897316]	[a1,a2,a3,a4,a6]
Generators	[2330635:10170927:6859]	Generators of the group modulo torsion
j	-1408000/243	j-invariant
L	5.4284384991373	L(r)(E,1)/r!
Ω	0.1406739406725	Real period
R	9.6471998885976	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8712h1 69696fk1 5808c1 17424p1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424o1

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	1	-	6	-4	1	-2	-6	3	7	-2	-4	-6	2	10	-1	3	-4	-3	-5	14	-16	13

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Quadratic twists for elliptic curve 17424o1

-4	8	-3	-11
8712h1	69696fk1	5808c1	17424p1

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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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