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	13013f	Isogeny class
Conductor	13013	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	266102837 = 7 · 113 · 134	Discriminant
Eigenvalues	-2  0  0 7+ 11- 13+ -2 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-845,-9422]	[a1,a2,a3,a4,a6]
Generators	[-17:5:1] [-16:1:1]	Generators of the group modulo torsion
j	2336256000/9317	j-invariant
L	3.4702284089556	L(r)(E,1)/r!
Ω	0.88570594324172	Real period
R	1.3060122400798	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	117117t1 91091s1 13013l1	Quadratic twists by: -3 -7 13

Hecke Eigenvalues for elliptic curve 13013f1

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	0	+	-	+	-2	-7	3	-8	-6	-7	-9	-4	-2	-9	-10	5	-12	7	-7	6	0	12	-14

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Quadratic twists for elliptic curve 13013f1

-3	-7	13
117117t1	91091s1	13013l1

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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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