Cremona's table of elliptic curves

3705 = 3 · 5 · 13 · 19

Field	Data	Notes
Atkin-Lehner	3+ 5- 13- 19+	Signs for the Atkin-Lehner involutions
Class	3705d	Isogeny class
Conductor	3705	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	5616	Modular degree for the optimal curve
Δ	-297418875 = -1 · 3 · 53 · 133 · 192	Discriminant
Eigenvalues	-2 3+ 5-  1  1 13- -1 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-9880,381306]	[a1,a2,a3,a4,a6]
Generators	[0:617:1]	Generators of the group modulo torsion
j	-106669068376969216/297418875	j-invariant
L	1.7736052703919	L(r)(E,1)/r!
Ω	1.5012247257726	Real period
R	0.065635493768048	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59280ch1 11115e1 18525l1 48165f1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3705d1

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
-2	+	-	1	1	-	-1	+	5	-8	6	-9	3	-10	-6	-11	4	5	-4	-9	-14	-5	6	9	5

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Quadratic twists for elliptic curve 3705d1

-4	-3	5	13	-19
59280ch1	11115e1	18525l1	48165f1	70395r1

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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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