Cremona's table of elliptic curves

1313 = 13 · 101

Field	Data	Notes
Atkin-Lehner	13+ 101+	Signs for the Atkin-Lehner involutions
Class	1313a	Isogeny class
Conductor	1313	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	88	Modular degree for the optimal curve
Δ	-1313 = -1 · 13 · 101	Discriminant
Eigenvalues	1 -3 -2  2  4 13+  3  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,2,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	658503/1313	j-invariant
L	1.9847408079224	L(r)(E,1)/r!
Ω	3.3341872424281	Real period
R	0.59526975050057	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	21008g1 84032p1 11817a1 32825f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1313a1

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

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Quadratic twists for elliptic curve 1313a1

-4	8	-3	5	-7	13
21008g1	84032p1	11817a1	32825f1	64337a1	17069b1

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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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