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	1785a	Isogeny class
Conductor	1785	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-106269975 = -1 · 36 · 52 · 73 · 17	Discriminant
Eigenvalues	1 3+ 5+ 7+ -4 -4 17-  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,77,-392]	[a1,a2,a3,a4,a6]
j	49471280711/106269975	j-invariant
L	0.97822517963137	L(r)(E,1)/r!
Ω	0.97822517963137	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28560dp1 114240ei1 5355k1 8925z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785a1

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	+	+	+	-4	-4	-	6	6	0	-4	-4	-2	4	6	14	-4	10	-4	4	10	-14	-2	0	-10

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Quadratic twists for elliptic curve 1785a1

-4	8	-3	5	-7	17
28560dp1	114240ei1	5355k1	8925z1	12495o1	30345bj1

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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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