Cremona's table of elliptic curves

5239 = 13² · 31

Field	Data	Notes
Atkin-Lehner	13+ 31+	Signs for the Atkin-Lehner involutions
Class	5239a	Isogeny class
Conductor	5239	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	936	Modular degree for the optimal curve
Δ	-27447121 = -1 · 134 · 312	Discriminant
Eigenvalues	1  0 -3  2  0 13+  5  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-116,573]	[a1,a2,a3,a4,a6]
Generators	[-4:33:1]	Generators of the group modulo torsion
j	-6073353/961	j-invariant
L	3.8147968256205	L(r)(E,1)/r!
Ω	2.0325599145628	Real period
R	0.93842174055694	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	83824w1 47151a1 5239b1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 5239a1

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	0	-3	2	0	+	5	4	4	3	+	-5	7	-2	-6	-9	-6	-1	10	-4	-3	2	-2	-6	-18

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Quadratic twists for elliptic curve 5239a1

-4	-3	13
83824w1	47151a1	5239b1

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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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