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	3705g	Isogeny class
Conductor	3705	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	351975 = 3 · 52 · 13 · 192	Discriminant
Eigenvalues	-1 3- 5+  0  0 13-  4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-206,-1155]	[a1,a2,a3,a4,a6]
j	967068262369/351975	j-invariant
L	1.260176150072	L(r)(E,1)/r!
Ω	1.260176150072	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	59280bc2 11115j2 18525b2 48165x2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3705g2

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	0	-	4	-	0	0	4	-2	-2	-2	2	2	-14	2	12	14	4	-14	6	2	-2

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Quadratic twists for elliptic curve 3705g2

-4	-3	5	13	-19
59280bc2	11115j2	18525b2	48165x2	70395b2

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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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