Cremona's table of elliptic curves

1833 = 3 · 13 · 47

Field	Data	Notes
Atkin-Lehner	3+ 13+ 47-	Signs for the Atkin-Lehner involutions
Class	1833a	Isogeny class
Conductor	1833	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	6480	Modular degree for the optimal curve
Δ	-343483525593 = -1 · 39 · 135 · 47	Discriminant
Eigenvalues	-1 3+  0 -1  5 13+  4  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-188403,31397538]	[a1,a2,a3,a4,a6]
j	-739583643739785288625/343483525593	j-invariant
L	0.78376967733285	L(r)(E,1)/r!
Ω	0.78376967733285	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	29328n1 117312bi1 5499e1 45825l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1833a1

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	+	0	-1	5	+	4	2	-6	3	-4	4	-8	4	-	12	2	7	8	-10	-5	16	14	-15	2

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Quadratic twists for elliptic curve 1833a1

-4	8	-3	5	-7	13	-47
29328n1	117312bi1	5499e1	45825l1	89817o1	23829a1	86151d1

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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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