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	1	Product of Tamagawa factors cp
Δ	-3428841728 = -1 · 28 · 13 · 1013	Discriminant
Eigenvalues	2-  1  0  2  0 13-  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2548,-50444]	[a1,a2,a3,a4,a6]
Generators	[65538837:1041738830:250047]	Generators of the group modulo torsion
j	-7149117778000/13393913	j-invariant
L	4.690216005704	L(r)(E,1)/r!
Ω	0.33593614859853	Real period
R	13.961629390796	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	21008i2 84032d2 47268g2 68276a2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5252b2

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 5252b2

-4	8	-3	13
21008i2	84032d2	47268g2	68276a2

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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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