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	17424bl	Isogeny class
Conductor	17424	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	-3974344704 = -1 · 212 · 36 · 113	Discriminant
Eigenvalues	2- 3-  3  0 11+  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1056,13552]	[a1,a2,a3,a4,a6]
Generators	[33:121:1]	Generators of the group modulo torsion
j	-32768	j-invariant
L	6.2480690527975	L(r)(E,1)/r!
Ω	1.3863396215093	Real period
R	2.2534409880009	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	1089e1 69696fh1 1936f1 17424bl2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bl1

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	0	+	0	0	0	-9	0	5	7	0	0	-12	-6	-15	0	-13	-3	0	0	0	9	17

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Quadratic twists for elliptic curve 17424bl1

-4	8	-3	-11
1089e1	69696fh1	1936f1	17424bl2

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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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