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	17360r	Isogeny class
Conductor	17360	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	-155545600 = -1 · 212 · 52 · 72 · 31	Discriminant
Eigenvalues	2-  2 5+ 7+  2 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-176,-1024]	[a1,a2,a3,a4,a6]
j	-148035889/37975	j-invariant
L	2.5854752523783	L(r)(E,1)/r!
Ω	0.64636881309458	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	1085c1 69440df1 86800by1 121520db1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 17360r1

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

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Quadratic twists for elliptic curve 17360r1

-4	8	5	-7
1085c1	69440df1	86800by1	121520db1

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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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