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	15840g	Isogeny class
Conductor	15840	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	-5845851000000 = -1 · 26 · 312 · 56 · 11	Discriminant
Eigenvalues	2+ 3- 5+ -4 11+  4  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-9993,-401708]	[a1,a2,a3,a4,a6]
j	-2365396076224/125296875	j-invariant
L	0.95207105871975	L(r)(E,1)/r!
Ω	0.23801776467994	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15840ba1 31680bz2 5280t1 79200ds1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15840g1

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	+	4	2	-6	4	-4	4	-6	0	-12	0	6	12	6	-4	-16	-4	-14	-10	14	-2

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Quadratic twists for elliptic curve 15840g1

-4	8	-3	5
15840ba1	31680bz2	5280t1	79200ds1

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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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