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	58800fl	Isogeny class
Conductor	58800	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	-4515840000000 = -1 · 217 · 32 · 57 · 72	Discriminant
Eigenvalues	2- 3+ 5+ 7-  1  7 -4  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-14408,-668688]	[a1,a2,a3,a4,a6]
Generators	[212:-2400:1]	Generators of the group modulo torsion
j	-105484561/1440	j-invariant
L	5.7474240162277	L(r)(E,1)/r!
Ω	0.21770250989073	Real period
R	0.82501116133902	Regulator
r	1	Rank of the group of rational points
S	0.99999999997633	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7350x1 11760cf1 58800ht1	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 58800fl1

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
-	+	+	-	1	7	-4	1	1	-8	6	3	-9	-4	3	1	12	4	12	14	-14	-4	-12	2	-16

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Quadratic twists for elliptic curve 58800fl1

-4	5	-7
7350x1	11760cf1	58800ht1

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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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