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	17360a	Isogeny class
Conductor	17360	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	184588880 = 24 · 5 · 74 · 312	Discriminant
Eigenvalues	2+ -2 5+ 7+  4  0  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3991,95724]	[a1,a2,a3,a4,a6]
j	439498833516544/11536805	j-invariant
L	1.6686884009574	L(r)(E,1)/r!
Ω	1.6686884009574	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8680f1 69440dk1 86800r1 121520s1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 17360a1

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	+	+	4	0	0	4	6	10	-	4	10	-2	12	12	-12	10	4	-16	4	-8	14	6	14

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Quadratic twists for elliptic curve 17360a1

-4	8	5	-7
8680f1	69440dk1	86800r1	121520s1

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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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