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	17424q	Isogeny class
Conductor	17424	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	43641285608448 = 210 · 37 · 117	Discriminant
Eigenvalues	2+ 3-  0  2 11-  0 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-9075,-98494]	[a1,a2,a3,a4,a6]
Generators	[-55:484:1]	Generators of the group modulo torsion
j	62500/33	j-invariant
L	5.4942496858844	L(r)(E,1)/r!
Ω	0.51904605041747	Real period
R	0.6615802299075	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	8712w1 69696fm1 5808e1 1584f1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424q1

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

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Quadratic twists for elliptic curve 17424q1

-4	8	-3	-11
8712w1	69696fm1	5808e1	1584f1

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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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