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	17424bk	Isogeny class
Conductor	17424	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	6867667648512 = 218 · 39 · 113	Discriminant
Eigenvalues	2- 3-  0  0 11+ -6 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5115,-62678]	[a1,a2,a3,a4,a6]
Generators	[-51:256:1]	Generators of the group modulo torsion
j	3723875/1728	j-invariant
L	4.6527309133072	L(r)(E,1)/r!
Ω	0.59028745960619	Real period
R	1.9705360657718	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	2178h1 69696ex1 5808z1 17424bj1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bk1

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

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Quadratic twists for elliptic curve 17424bk1

-4	8	-3	-11
2178h1	69696ex1	5808z1	17424bj1

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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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