Cremona's table of elliptic curves

13005 = 3² · 5 · 17²

Field	Data	Notes
Atkin-Lehner	3- 5- 17+	Signs for the Atkin-Lehner involutions
Class	13005m	Isogeny class
Conductor	13005	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2592	Modular degree for the optimal curve
Δ	26335125 = 36 · 53 · 172	Discriminant
Eigenvalues	0 3- 5- -2 -3  2 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-102,310]	[a1,a2,a3,a4,a6]
Generators	[-2:22:1]	Generators of the group modulo torsion
j	557056/125	j-invariant
L	3.4871445160176	L(r)(E,1)/r!
Ω	1.9931226710556	Real period
R	0.29159808430747	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	1445a1 65025bf1 13005l1	Quadratic twists by: -3 5 17

Hecke Eigenvalues for elliptic curve 13005m1

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	-	-	-2	-3	2	+	-7	6	-3	-8	4	9	2	12	0	9	7	-16	-3	16	1	12	-9	-2

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Quadratic twists for elliptic curve 13005m1

-3	5	17
1445a1	65025bf1	13005l1

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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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