Cremona's table of elliptic curves

58800 = 2⁴ · 3 · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7+	Signs for the Atkin-Lehner involutions
Class	58800eb	Isogeny class
Conductor	58800	Conductor
∏ cp	27	Product of Tamagawa factors cp
deg	241920	Modular degree for the optimal curve
Δ	-972810168750000 = -1 · 24 · 33 · 58 · 78	Discriminant
Eigenvalues	2+ 3- 5- 7+ -4  1  6 -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-28583,-2399412]	[a1,a2,a3,a4,a6]
Generators	[408:7350:1]	Generators of the group modulo torsion
j	-71680/27	j-invariant
L	7.2806792820738	L(r)(E,1)/r!
Ω	0.18020725793793	Real period
R	1.4963591994571	Regulator
r	1	Rank of the group of rational points
S	1.0000000000022	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	29400y1 58800k1 58800cg1	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 58800eb1

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
+	-	-	+	-4	1	6	-3	-6	0	0	3	-4	0	-6	6	-2	11	7	4	-11	-15	-6	14	1

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Quadratic twists for elliptic curve 58800eb1

-4	5	-7
29400y1	58800k1	58800cg1

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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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