Cremona's table of elliptic curves

5031 = 3² · 13 · 43

Field	Data	Notes
Atkin-Lehner	3- 13+ 43-	Signs for the Atkin-Lehner involutions
Class	5031d	Isogeny class
Conductor	5031	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3861981747 = 312 · 132 · 43	Discriminant
Eigenvalues	1 3- -2  0  4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1998,34749]	[a1,a2,a3,a4,a6]
Generators	[-36:261:1]	Generators of the group modulo torsion
j	1210333063393/5297643	j-invariant
L	4.0821907406951	L(r)(E,1)/r!
Ω	1.4023133967528	Real period
R	1.4555201248693	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	80496bd2 1677b2 125775v2 65403m2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5031d2

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	-	-2	0	4	+	2	-4	6	0	2	-4	6	-	-4	-2	-4	6	-2	8	4	-12	-8	-6	-6

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Quadratic twists for elliptic curve 5031d2

-4	-3	5	13
80496bd2	1677b2	125775v2	65403m2

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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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