Cremona's table of elliptic curves

1785 = 3 · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 17+	Signs for the Atkin-Lehner involutions
Class	1785j	Isogeny class
Conductor	1785	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-1534698375 = -1 · 3 · 53 · 72 · 174	Discriminant
Eigenvalues	1 3- 5+ 7-  0 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,286,287]	[a1,a2,a3,a4,a6]
Generators	[165:1192:27]	Generators of the group modulo torsion
j	2600176603751/1534698375	j-invariant
L	3.9002053811488	L(r)(E,1)/r!
Ω	0.9167568733842	Real period
R	4.2543508474075	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28560ce1 114240ca1 5355r1 8925e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785j1

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	-2	+	-4	-8	2	-8	2	6	-8	-8	2	4	-2	-8	-4	-2	-8	-12	10	-10

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Quadratic twists for elliptic curve 1785j1

-4	8	-3	5	-7	17
28560ce1	114240ca1	5355r1	8925e1	12495f1	30345j1

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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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