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	17360bl	Isogeny class
Conductor	17360	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	31104	Modular degree for the optimal curve
Δ	56885248000 = 221 · 53 · 7 · 31	Discriminant
Eigenvalues	2-  3 5- 7- -1 -5 -4 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4507,-115894]	[a1,a2,a3,a4,a6]
Generators	[-1041:640:27]	Generators of the group modulo torsion
j	2471874619761/13888000	j-invariant
L	9.078548851152	L(r)(E,1)/r!
Ω	0.58287387636162	Real period
R	1.2979578743835	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	2170o1 69440db1 86800bl1 121520bp1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 17360bl1

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
-	3	-	-	-1	-5	-4	-3	-3	2	-	-8	-10	0	-5	-2	-3	0	4	5	-4	4	1	-15	-19

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Quadratic twists for elliptic curve 17360bl1

-4	8	5	-7
2170o1	69440db1	86800bl1	121520bp1

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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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