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	15840c	Isogeny class
Conductor	15840	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	86016	Modular degree for the optimal curve
Δ	-7425456060369600 = -1 · 26 · 320 · 52 · 113	Discriminant
Eigenvalues	2+ 3- 5+  0 11+ -4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-16833,4230268]	[a1,a2,a3,a4,a6]
j	-11305786504384/159153293475	j-invariant
L	1.4152739337522	L(r)(E,1)/r!
Ω	0.35381848343805	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	15840x1 31680bs2 5280q1 79200de1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15840c1

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

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Quadratic twists for elliptic curve 15840c1

-4	8	-3	5
15840x1	31680bs2	5280q1	79200de1

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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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