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	5252a	Isogeny class
Conductor	5252	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	552	Modular degree for the optimal curve
Δ	273104 = 24 · 132 · 101	Discriminant
Eigenvalues	2-  2 -2  0  0 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-29,-46]	[a1,a2,a3,a4,a6]
Generators	[-430:138:125]	Generators of the group modulo torsion
j	174456832/17069	j-invariant
L	4.7266434660248	L(r)(E,1)/r!
Ω	2.064349152067	Real period
R	4.5793062295611	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	21008h1 84032i1 47268c1 68276d1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5252a1

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
-	2	-2	0	0	+	6	-4	-4	-2	8	10	-12	0	0	2	8	-14	-8	-16	-4	0	16	-12	2

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Quadratic twists for elliptic curve 5252a1

-4	8	-3	13
21008h1	84032i1	47268c1	68276d1

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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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