Cremona's table of elliptic curves

17520 = 2⁴ · 3 · 5 · 73

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 73+	Signs for the Atkin-Lehner involutions
Class	17520r	Isogeny class
Conductor	17520	Conductor
∏ cp	56	Product of Tamagawa factors cp
deg	56448	Modular degree for the optimal curve
Δ	-357536498688000 = -1 · 213 · 314 · 53 · 73	Discriminant
Eigenvalues	2- 3- 5+  2  2  0  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-18136,1302164]	[a1,a2,a3,a4,a6]
Generators	[62:648:1]	Generators of the group modulo torsion
j	-161069099939929/87289184250	j-invariant
L	6.3842571760439	L(r)(E,1)/r!
Ω	0.50000938071846	Real period
R	0.22800490715903	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	2190a1 70080bq1 52560bd1 87600bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17520r1

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
-	-	+	2	2	0	3	-5	3	5	-5	-7	-5	-11	0	-12	-2	-6	-2	-8	+	-2	16	-17	-10

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Quadratic twists for elliptic curve 17520r1

-4	8	-3	5
2190a1	70080bq1	52560bd1	87600bp1

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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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