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	1785n	Isogeny class
Conductor	1785	Conductor
∏ cp	84	Product of Tamagawa factors cp
deg	20160	Modular degree for the optimal curve
Δ	-742780064187984375 = -1 · 314 · 56 · 7 · 175	Discriminant
Eigenvalues	1 3- 5- 7-  0  4 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,115937,-38571787]	[a1,a2,a3,a4,a6]
j	172343644217341694999/742780064187984375	j-invariant
L	3.0224049494937	L(r)(E,1)/r!
Ω	0.14392404521399	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	28560co1 114240v1 5355j1 8925f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785n1

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

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Quadratic twists for elliptic curve 1785n1

-4	8	-3	5	-7	17
28560co1	114240v1	5355j1	8925f1	12495c1	30345a1

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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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