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	15840y	Isogeny class
Conductor	15840	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	100800	Modular degree for the optimal curve
Δ	-22729836254400000 = -1 · 29 · 36 · 55 · 117	Discriminant
Eigenvalues	2- 3- 5+  1 11- -2  5  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-27003,7452002]	[a1,a2,a3,a4,a6]
j	-5833944216008/60897409375	j-invariant
L	2.2704284902303	L(r)(E,1)/r!
Ω	0.32434692717576	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15840t1 31680di1 1760d1 79200bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15840y1

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
-	-	+	1	-	-2	5	7	-6	1	5	11	-2	-4	6	1	-10	5	8	9	-6	10	-6	-17	16

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Quadratic twists for elliptic curve 15840y1

-4	8	-3	5
15840t1	31680di1	1760d1	79200bl1

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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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