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	1833d	Isogeny class
Conductor	1833	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1680	Modular degree for the optimal curve
Δ	4263699141 = 35 · 132 · 473	Discriminant
Eigenvalues	-2 3+ -1 -1  1 13-  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-3216,71210]	[a1,a2,a3,a4,a6]
Generators	[-7:305:1]	Generators of the group modulo torsion
j	3679653013295104/4263699141	j-invariant
L	1.201277501659	L(r)(E,1)/r!
Ω	1.3790921717231	Real period
R	0.1451773282804	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	29328t1 117312bd1 5499h1 45825j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1833d1

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

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Quadratic twists for elliptic curve 1833d1

-4	8	-3	5	-7	13	-47
29328t1	117312bd1	5499h1	45825j1	89817k1	23829c1	86151c1

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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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