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	17520k	Isogeny class
Conductor	17520	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	10368	Modular degree for the optimal curve
Δ	-58853744640 = -1 · 213 · 39 · 5 · 73	Discriminant
Eigenvalues	2- 3+ 5+  1  0 -4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-216,-11664]	[a1,a2,a3,a4,a6]
Generators	[74:610:1]	Generators of the group modulo torsion
j	-273359449/14368590	j-invariant
L	3.7058119189396	L(r)(E,1)/r!
Ω	0.48792402597962	Real period
R	3.797529657921	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	2190d1 70080cp1 52560bh1 87600ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17520k1

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
-	+	+	1	0	-4	0	-2	-3	6	4	-7	-6	10	0	3	0	8	13	6	-	1	15	-6	-10

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Quadratic twists for elliptic curve 17520k1

-4	8	-3	5
2190d1	70080cp1	52560bh1	87600ca1

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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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