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	17360bb	Isogeny class
Conductor	17360	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	144000	Modular degree for the optimal curve
Δ	218530368716800000 = 227 · 55 · 75 · 31	Discriminant
Eigenvalues	2-  1 5- 7+  3 -1 -2  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-159920,9949268]	[a1,a2,a3,a4,a6]
Generators	[-334:5120:1]	Generators of the group modulo torsion
j	110426885440588081/53352140800000	j-invariant
L	6.13529217328	L(r)(E,1)/r!
Ω	0.28050995641025	Real period
R	1.0935961510591	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	2170q1 69440cf1 86800bu1 121520bx1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 17360bb1

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	-	+	3	-1	-2	5	1	-10	+	-2	-8	-4	7	4	5	12	12	3	4	-10	-9	5	-17

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Quadratic twists for elliptic curve 17360bb1

-4	8	5	-7
2170q1	69440cf1	86800bu1	121520bx1

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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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