Cremona's table of elliptic curves

17325 = 3² · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	17325o	Isogeny class
Conductor	17325	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	74882825325 = 38 · 52 · 73 · 113	Discriminant
Eigenvalues	0 3- 5+ 7+ 11- -5  3  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-8490,300811]	[a1,a2,a3,a4,a6]
Generators	[49:49:1]	Generators of the group modulo torsion
j	3713464238080/4108797	j-invariant
L	3.6521480987698	L(r)(E,1)/r!
Ω	1.0856019464169	Real period
R	0.56069478486473	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	5775b2 17325bu2 121275ea2	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 17325o2

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
0	-	+	+	-	-5	3	5	0	-6	-4	7	-3	4	-12	9	-6	-1	-5	15	-11	-10	0	-12	16

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Quadratic twists for elliptic curve 17325o2

-3	5	-7
5775b2	17325bu2	121275ea2

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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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