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	4800c	Isogeny class
Conductor	4800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	82944000000 = 216 · 34 · 56	Discriminant
Eigenvalues	2+ 3+ 5+  0 -4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2433,-43263]	[a1,a2,a3,a4,a6]
Generators	[-24:27:1]	Generators of the group modulo torsion
j	1556068/81	j-invariant
L	3.0685342177209	L(r)(E,1)/r!
Ω	0.68195012558917	Real period
R	2.2498230461281	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4800cb4 600d3 14400x4 192c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4800c3

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	8	-6	8	6	-6	4	0	-2	-4	2	-4	8	-10	-8	-4	-6	-2

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Quadratic twists for elliptic curve 4800c3

-4	8	-3	5
4800cb4	600d3	14400x4	192c3

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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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