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	1786f	Isogeny class
Conductor	1786	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	2640	Modular degree for the optimal curve
Δ	-1375305728 = -1 · 215 · 19 · 472	Discriminant
Eigenvalues	2-  1 -2  3 -6 -5 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-4899,131585]	[a1,a2,a3,a4,a6]
Generators	[-2:377:1]	Generators of the group modulo torsion
j	-13003239781926577/1375305728	j-invariant
L	4.2991569253826	L(r)(E,1)/r!
Ω	1.4587882328362	Real period
R	0.098235801208426	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	14288d1 57152e1 16074b1 44650b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1786f1

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	-6	-5	-5	+	-7	3	10	10	-12	2	-	9	-7	8	-1	8	11	-6	14	-4	-12

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Quadratic twists for elliptic curve 1786f1

-4	8	-3	5	-7	-19	-47
14288d1	57152e1	16074b1	44650b1	87514r1	33934g1	83942j1

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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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