Cremona's table of elliptic curves

4800 = 2⁶ · 3 · 5²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+	Signs for the Atkin-Lehner involutions
Class	4800b	Isogeny class
Conductor	4800	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	61440000000 = 218 · 3 · 57	Discriminant
Eigenvalues	2+ 3+ 5+  0  4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-128033,17675937]	[a1,a2,a3,a4,a6]
Generators	[297:2400:1]	Generators of the group modulo torsion
j	56667352321/15	j-invariant
L	3.2907346725662	L(r)(E,1)/r!
Ω	0.88581914230645	Real period
R	0.92872645086389	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	4800cd3 75b4 14400y3 960g4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4800b4

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

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Quadratic twists for elliptic curve 4800b4

-4	8	-3	5
4800cd3	75b4	14400y3	960g4

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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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