Cremona's table of elliptic curves

1786 = 2 · 19 · 47

Field	Data	Notes
Atkin-Lehner	2+ 19+ 47-	Signs for the Atkin-Lehner involutions
Class	1786a	Isogeny class
Conductor	1786	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-83942 = -1 · 2 · 19 · 472	Discriminant
Eigenvalues	2+  1  2  1  4  5 -1 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-30,-66]	[a1,a2,a3,a4,a6]
j	-2845178713/83942	j-invariant
L	2.0446198985528	L(r)(E,1)/r!
Ω	1.0223099492764	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	14288b1 57152g1 16074g1 44650m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1786a1

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	1	4	5	-1	+	3	1	4	6	0	-8	-	7	-3	4	3	6	7	-4	4	-14	-10

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Quadratic twists for elliptic curve 1786a1

-4	8	-3	5	-7	-19	-47
14288b1	57152g1	16074g1	44650m1	87514e1	33934l1	83942f1

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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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