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	1785l	Isogeny class
Conductor	1785	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	528	Modular degree for the optimal curve
Δ	-125355195 = -1 · 36 · 5 · 7 · 173	Discriminant
Eigenvalues	0 3- 5+ 7- -6 -1 17-  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-141,-889]	[a1,a2,a3,a4,a6]
j	-312217698304/125355195	j-invariant
L	1.3577785848007	L(r)(E,1)/r!
Ω	0.67888929240033	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	28560cm1 114240cp1 5355o1 8925a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785l1

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
0	-	+	-	-6	-1	-	2	3	0	5	5	9	8	-9	0	0	5	8	6	-16	2	3	6	2

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Quadratic twists for elliptic curve 1785l1

-4	8	-3	5	-7	17
28560cm1	114240cp1	5355o1	8925a1	12495d1	30345i1

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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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