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	17360d	Isogeny class
Conductor	17360	Conductor
∏ cp	72	Product of Tamagawa factors cp
deg	1161216	Modular degree for the optimal curve
Δ	-4.4054054065557E+22	Discriminant
Eigenvalues	2+  1 5+ 7- -3  1  3  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8230881,13583553755]	[a1,a2,a3,a4,a6]
Generators	[1174:74431:1]	Generators of the group modulo torsion
j	-240892216689399984415744/172086148693581998435	j-invariant
L	5.4650220636876	L(r)(E,1)/r!
Ω	0.10490057769001	Real period
R	0.72357165126569	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	8680a1 69440du1 86800h1 121520m1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 17360d1

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	3	6	-2	-1	-	-10	8	10	-11	-4	0	4	-12	-8	-6	11	-4	0	-17

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Quadratic twists for elliptic curve 17360d1

-4	8	5	-7
8680a1	69440du1	86800h1	121520m1

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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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