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	39200bc	Isogeny class
Conductor	39200	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-25088000 = -1 · 212 · 53 · 72	Discriminant
Eigenvalues	2+ -1 5- 7-  4 -2 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,47,-223]	[a1,a2,a3,a4,a6]
Generators	[7:20:1]	Generators of the group modulo torsion
j	448	j-invariant
L	4.2622015785936	L(r)(E,1)/r!
Ω	1.1013330160072	Real period
R	0.96750971700741	Regulator
r	1	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	39200cs1 78400eo1 39200cr1 39200u1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 39200bc1

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	-	-	4	-2	-6	6	-5	-9	2	-4	3	1	8	-14	6	1	5	14	-2	10	-3	-9	-8

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Quadratic twists for elliptic curve 39200bc1

-4	8	5	-7
39200cs1	78400eo1	39200cr1	39200u1

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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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