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	15840k	Isogeny class
Conductor	15840	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	320760000000000 = 212 · 36 · 510 · 11	Discriminant
Eigenvalues	2+ 3- 5+  0 11-  4  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-38028,-2721152]	[a1,a2,a3,a4,a6]
Generators	[-114:364:1]	Generators of the group modulo torsion
j	2036792051776/107421875	j-invariant
L	4.8572153072099	L(r)(E,1)/r!
Ω	0.34300173244049	Real period
R	3.540226511868	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15840b2 31680df1 1760l2 79200dw2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15840k2

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	4	-4	2	-6	-4	2	2	-4	-2	-2	-4	-2	-10	8	4	-16	-4	10	-18

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Quadratic twists for elliptic curve 15840k2

-4	8	-3	5
15840b2	31680df1	1760l2	79200dw2

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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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