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	16	Product of Tamagawa factors cp
Δ	1066535656875 = 312 · 54 · 132 · 19	Discriminant
Eigenvalues	-1 3+ 5- -4  0 13+  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-17505,-897348]	[a1,a2,a3,a4,a6]
Generators	[-78:71:1]	Generators of the group modulo torsion
j	593214295178117521/1066535656875	j-invariant
L	1.7047708279366	L(r)(E,1)/r!
Ω	0.41510293012848	Real period
R	1.0267157277166	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	59280bv4 11115d4 18525o3 48165c4	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3705c3

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 3705c3

-4	-3	5	13	-19
59280bv4	11115d4	18525o3	48165c4	70395s4

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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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