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	58800di	Isogeny class
Conductor	58800	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	147456	Modular degree for the optimal curve
Δ	-83383728750000 = -1 · 24 · 34 · 57 · 77	Discriminant
Eigenvalues	2+ 3- 5+ 7-  4  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,10617,128988]	[a1,a2,a3,a4,a6]
Generators	[2088:95550:1]	Generators of the group modulo torsion
j	4499456/2835	j-invariant
L	8.4528839577715	L(r)(E,1)/r!
Ω	0.37707932636698	Real period
R	2.802090756107	Regulator
r	1	Rank of the group of rational points
S	0.99999999999001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	29400q1 11760p1 8400i1	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 58800di1

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

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Quadratic twists for elliptic curve 58800di1

-4	5	-7
29400q1	11760p1	8400i1

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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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