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	15840b	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]
j	2036792051776/107421875	j-invariant
L	2.1420180017997	L(r)(E,1)/r!
Ω	0.53550450044992	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	15840k2 31680dx1 1760n2 79200df2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15840b2

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 15840b2

-4	8	-3	5
15840k2	31680dx1	1760n2	79200df2

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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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