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	1786b	Isogeny class
Conductor	1786	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	-15796501371608 = -1 · 23 · 197 · 472	Discriminant
Eigenvalues	2+  1 -2 -3  0  1  7 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,5893,79486]	[a1,a2,a3,a4,a6]
j	22638047668438103/15796501371608	j-invariant
L	0.88279945191585	L(r)(E,1)/r!
Ω	0.44139972595792	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	14288c1 57152f1 16074f1 44650n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1786b1

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	-3	0	1	7	+	-1	-3	4	-2	0	8	-	3	5	8	11	14	-1	0	8	14	6

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Quadratic twists for elliptic curve 1786b1

-4	8	-3	5	-7	-19	-47
14288c1	57152f1	16074f1	44650n1	87514d1	33934m1	83942e1

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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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