Cremona's table of elliptic curves

5848 = 2³ · 17 · 43

Field	Data	Notes
Atkin-Lehner	2+ 17+ 43+	Signs for the Atkin-Lehner involutions
Class	5848a	Isogeny class
Conductor	5848	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	2325539072 = 28 · 173 · 432	Discriminant
Eigenvalues	2+  2 -4  2  0  6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1580,24596]	[a1,a2,a3,a4,a6]
Generators	[13:78:1]	Generators of the group modulo torsion
j	1705021456336/9084137	j-invariant
L	4.6471767784432	L(r)(E,1)/r!
Ω	1.4633214470495	Real period
R	3.1757730249996	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	11696c1 46784i1 52632q1 99416b1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 5848a1

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

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Quadratic twists for elliptic curve 5848a1

-4	8	-3	17
11696c1	46784i1	52632q1	99416b1

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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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