Cremona's table of elliptic curves

5252 = 2² · 13 · 101

Field	Data	Notes
Atkin-Lehner	2- 13- 101+	Signs for the Atkin-Lehner involutions
Class	5252b	Isogeny class
Conductor	5252	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-56805632 = -1 · 28 · 133 · 101	Discriminant
Eigenvalues	2-  1  0  2  0 13-  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,52,-316]	[a1,a2,a3,a4,a6]
Generators	[260:4202:1]	Generators of the group modulo torsion
j	59582000/221897	j-invariant
L	4.690216005704	L(r)(E,1)/r!
Ω	1.0078084457956	Real period
R	4.6538764635986	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	21008i1 84032d1 47268g1 68276a1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5252b1

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	2	0	-	3	-1	-6	-6	-4	-4	-3	-4	0	-6	0	8	-4	9	-7	8	6	9	8

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Quadratic twists for elliptic curve 5252b1

-4	8	-3	13
21008i1	84032d1	47268g1	68276a1

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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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