Cremona's table of elliptic curves

5088 = 2⁵ · 3 · 53

Field	Data	Notes
Atkin-Lehner	2- 3- 53-	Signs for the Atkin-Lehner involutions
Class	5088f	Isogeny class
Conductor	5088	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	732672 = 29 · 33 · 53	Discriminant
Eigenvalues	2- 3- -2  4  0  6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-15264,720792]	[a1,a2,a3,a4,a6]
j	768222946338056/1431	j-invariant
L	2.7694883645448	L(r)(E,1)/r!
Ω	1.8463255763632	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5088b2 10176a4 15264d2 127200d4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5088f3

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	0	6	-6	4	0	-2	8	-2	6	4	0	-	8	-6	12	-8	2	-8	-4	2	2

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Quadratic twists for elliptic curve 5088f3

-4	8	-3	5
5088b2	10176a4	15264d2	127200d4

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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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