Cremona's table of elliptic curves

39200 = 2⁵ · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7-	Signs for the Atkin-Lehner involutions
Class	39200p	Isogeny class
Conductor	39200	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	16128	Modular degree for the optimal curve
Δ	-1960000000 = -1 · 29 · 57 · 72	Discriminant
Eigenvalues	2+ -2 5+ 7- -3 -1 -2 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-408,3688]	[a1,a2,a3,a4,a6]
Generators	[-22:50:1] [18:50:1]	Generators of the group modulo torsion
j	-19208/5	j-invariant
L	6.4187221229095	L(r)(E,1)/r!
Ω	1.4043334290923	Real period
R	0.57133174269172	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	39200cb1 78400cf1 7840s1 39200c1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 39200p1

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
+	-2	+	-	-3	-1	-2	-1	1	-2	-4	-9	-3	-2	-9	-9	0	-12	8	-16	4	-6	4	-6	18

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Quadratic twists for elliptic curve 39200p1

-4	8	5	-7
39200cb1	78400cf1	7840s1	39200c1

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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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