Cremona's table of elliptic curves

39520 = 2⁵ · 5 · 13 · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 13- 19+	Signs for the Atkin-Lehner involutions
Class	39520f	Isogeny class
Conductor	39520	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	24064	Modular degree for the optimal curve
Δ	7047759680 = 26 · 5 · 132 · 194	Discriminant
Eigenvalues	2- -2 5+ -2  0 13-  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1006,-11940]	[a1,a2,a3,a4,a6]
Generators	[-19:26:1]	Generators of the group modulo torsion
j	1761040374976/110121245	j-invariant
L	2.892285823379	L(r)(E,1)/r!
Ω	0.85096589594205	Real period
R	1.6994134765975	Regulator
r	1	Rank of the group of rational points
S	1.0000000000005	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	39520b1 79040z2	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 39520f1

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	+	-2	0	-	2	+	6	-2	-8	-2	6	-6	-2	-10	12	2	14	8	-14	0	-2	10	-10

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Quadratic twists for elliptic curve 39520f1

-4	8
39520b1	79040z2

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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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