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	12	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-552491415 = -1 · 33 · 5 · 72 · 174	Discriminant
Eigenvalues	1 3- 5+ 7+  0  6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,41,-1123]	[a1,a2,a3,a4,a6]
j	7892485271/552491415	j-invariant
L	2.3459740913709	L(r)(E,1)/r!
Ω	0.78199136379032	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	28560cn1 114240bo1 5355m1 8925i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785i1

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 1785i1

-4	8	-3	5	-7	17
28560cn1	114240bo1	5355m1	8925i1	12495g1	30345p1

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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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