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	3705c	Isogeny class
Conductor	3705	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2112	Modular degree for the optimal curve
Δ	-2973273615 = -1 · 33 · 5 · 132 · 194	Discriminant
Eigenvalues	-1 3+ 5- -4  0 13+  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,355,-358]	[a1,a2,a3,a4,a6]
Generators	[50:356:1]	Generators of the group modulo torsion
j	4946890630319/2973273615	j-invariant
L	1.7047708279366	L(r)(E,1)/r!
Ω	0.83020586025696	Real period
R	4.1068629108665	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	59280bv1 11115d1 18525o1 48165c1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3705c1

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

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Quadratic twists for elliptic curve 3705c1

-4	-3	5	13	-19
59280bv1	11115d1	18525o1	48165c1	70395s1

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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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