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	13005b	Isogeny class
Conductor	13005	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-941727254535 = -1 · 33 · 5 · 178	Discriminant
Eigenvalues	-1 3+ 5+ -4  2  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-4823,-135898]	[a1,a2,a3,a4,a6]
Generators	[1356:49174:1]	Generators of the group modulo torsion
j	-19034163/1445	j-invariant
L	2.2012413147505	L(r)(E,1)/r!
Ω	0.28520544620422	Real period
R	3.8590450218373	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13005e1 65025f1 765b1	Quadratic twists by: -3 5 17

Hecke Eigenvalues for elliptic curve 13005b1

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	+	+	-4	2	2	+	0	0	6	-8	-8	-2	-2	0	10	4	-10	2	-14	8	8	-4	0	16

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Quadratic twists for elliptic curve 13005b1

-3	5	17
13005e1	65025f1	765b1

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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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