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	1785k	Isogeny class
Conductor	1785	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-669375 = -1 · 32 · 54 · 7 · 17	Discriminant
Eigenvalues	-1 3- 5+ 7-  0 -6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,14,35]	[a1,a2,a3,a4,a6]
Generators	[-1:5:1]	Generators of the group modulo torsion
j	302111711/669375	j-invariant
L	2.1569213922132	L(r)(E,1)/r!
Ω	1.9943115779429	Real period
R	1.0815368150438	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28560cf1 114240cd1 5355q1 8925d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785k1

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	-2	0	-6	-10	4	4	6	4	-14	-12	12	-10	-12	16	-6	-18

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Quadratic twists for elliptic curve 1785k1

-4	8	-3	5	-7	17
28560cf1	114240cd1	5355q1	8925d1	12495h1	30345m1

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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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