Cremona's table of elliptic curves

13013 = 7 · 11 · 13²

Field	Data	Notes
Atkin-Lehner	7+ 11- 13+	Signs for the Atkin-Lehner involutions
Class	13013d	Isogeny class
Conductor	13013	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	139776	Modular degree for the optimal curve
Δ	7389682576809533 = 77 · 11 · 138	Discriminant
Eigenvalues	2  0  4 7+ 11- 13+ -2  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-63713,4605461]	[a1,a2,a3,a4,a6]
j	35063967744/9058973	j-invariant
L	6.2590998803932	L(r)(E,1)/r!
Ω	0.39119374252457	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	117117x1 91091q1 13013n1	Quadratic twists by: -3 -7 13

Hecke Eigenvalues for elliptic curve 13013d1

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	0	4	+	-	+	-2	5	3	0	2	9	3	0	10	-1	-6	1	-12	15	5	-6	8	4	-2

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Quadratic twists for elliptic curve 13013d1

-3	-7	13
117117x1	91091q1	13013n1

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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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