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	1785i	Isogeny class
Conductor	1785	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	2213451765 = 312 · 5 · 72 · 17	Discriminant
Eigenvalues	1 3- 5+ 7+  0  6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-22229,-1277449]	[a1,a2,a3,a4,a6]
j	1214661886599131209/2213451765	j-invariant
L	2.3459740913709	L(r)(E,1)/r!
Ω	0.39099568189516	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	28560cn4 114240bo4 5355m4 8925i3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785i3

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	6	+	4	0	-6	8	10	6	-8	0	2	4	-2	8	12	14	0	12	-14	-10

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Quadratic twists for elliptic curve 1785i3

-4	8	-3	5	-7	17
28560cn4	114240bo4	5355m4	8925i3	12495g4	30345p4

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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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