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	5088b	Isogeny class
Conductor	5088	Conductor
∏ cp	1	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	0.42951673969382	L(r)(E,1)/r!
Ω	0.42951673969382	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5088f3 10176f3 15264n3 127200dd4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5088b2

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 5088b2

-4	8	-3	5
5088f3	10176f3	15264n3	127200dd4

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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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