Cremona's table of elliptic curves

15840 = 2⁵ · 3² · 5 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	15840z	Isogeny class
Conductor	15840	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	1270209600 = 26 · 38 · 52 · 112	Discriminant
Eigenvalues	2- 3- 5+  4 11-  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-273,272]	[a1,a2,a3,a4,a6]
j	48228544/27225	j-invariant
L	2.6384991759454	L(r)(E,1)/r!
Ω	1.3192495879727	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	15840v1 31680do2 5280c1 79200bx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15840z1

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	-4	0	-6	8	2	2	-4	0	-6	4	2	-4	-12	14	8	8	14	10

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Quadratic twists for elliptic curve 15840z1

-4	8	-3	5
15840v1	31680do2	5280c1	79200bx1

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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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