Cremona's table of elliptic curves

17360 = 2⁴ · 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2+ 5- 7+ 31-	Signs for the Atkin-Lehner involutions
Class	17360m	Isogeny class
Conductor	17360	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	-476358400 = -1 · 28 · 52 · 74 · 31	Discriminant
Eigenvalues	2+  0 5- 7+ -4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,193,-194]	[a1,a2,a3,a4,a6]
Generators	[37:240:1]	Generators of the group modulo torsion
j	3105672624/1860775	j-invariant
L	4.4544089774871	L(r)(E,1)/r!
Ω	0.9681100335715	Real period
R	2.3005695752652	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	8680o1 69440cj1 86800p1 121520c1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 17360m1

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	-	+	-4	-2	-2	4	4	10	-	2	-6	-4	8	10	-4	-2	-12	0	-2	-4	-16	-18	18

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Quadratic twists for elliptic curve 17360m1

-4	8	5	-7
8680o1	69440cj1	86800p1	121520c1

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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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