Cremona's table of elliptic curves

48841 = 13² · 17²

Field	Data	Notes
Atkin-Lehner	13+ 17+	Signs for the Atkin-Lehner involutions
Class	48841d	Isogeny class
Conductor	48841	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	86016	Modular degree for the optimal curve
Δ	4007685032273 = 138 · 173	Discriminant
Eigenvalues	1 -2  2  0  0 13+ 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-12510,528803]	[a1,a2,a3,a4,a6]
Generators	[143:1220:1]	Generators of the group modulo torsion
j	9129329/169	j-invariant
L	5.4879004105152	L(r)(E,1)/r!
Ω	0.7828037555748	Real period
R	3.5052849270484	Regulator
r	1	Rank of the group of rational points
S	1.0000000000016	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3757d1 48841c1	Quadratic twists by: 13 17

Hecke Eigenvalues for elliptic curve 48841d1

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

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Quadratic twists for elliptic curve 48841d1

13	17
3757d1	48841c1

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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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