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	58800gr	Isogeny class
Conductor	58800	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1494236419200000000 = 213 · 34 · 58 · 78	Discriminant
Eigenvalues	2- 3+ 5- 7+ -6 -4 -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2813100208,57429232078912]	[a1,a2,a3,a4,a6]
Generators	[30688:19944:1]	Generators of the group modulo torsion
j	266916252066900625/162	j-invariant
L	3.3782733875487	L(r)(E,1)/r!
Ω	0.11560167302547	Real period
R	3.6529244119701	Regulator
r	1	Rank of the group of rational points
S	0.99999999996271	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7350cu2 58800ia2 58800kh2	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 58800gr2

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
-	+	-	+	-6	-4	-3	4	-3	-6	-5	8	-3	-8	-9	12	-6	2	-8	9	14	7	6	3	17

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Quadratic twists for elliptic curve 58800gr2

-4	5	-7
7350cu2	58800ia2	58800kh2

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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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