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	4800r	Isogeny class
Conductor	4800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-33592320000000 = -1 · 216 · 38 · 57	Discriminant
Eigenvalues	2+ 3- 5+  0  4  6  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,7967,56063]	[a1,a2,a3,a4,a6]
j	54607676/32805	j-invariant
L	3.211594715932	L(r)(E,1)/r!
Ω	0.4014493394915	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	4800bi4 600a4 14400z4 960b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4800r4

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	6	6	4	0	2	-8	-2	-6	12	-8	6	-12	-14	4	8	6	-8	-12	10	-2

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Quadratic twists for elliptic curve 4800r4

-4	8	-3	5
4800bi4	600a4	14400z4	960b4

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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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