Cremona's table of elliptic curves

3698 = 2 · 43²

Field	Data	Notes
Atkin-Lehner	2+ 43+	Signs for the Atkin-Lehner involutions
Class	3698a	Isogeny class
Conductor	3698	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	47874868337053696 = 212 · 438	Discriminant
Eigenvalues	2+  1  3 -1  0 -1  3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-429007,-107676542]	[a1,a2,a3,a4,a6]
Generators	[-506891:1199468:1331]	Generators of the group modulo torsion
j	747081097/4096	j-invariant
L	3.4650598460247	L(r)(E,1)/r!
Ω	0.18660657651079	Real period
R	3.0947996857124	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	29584j2 118336f2 33282y2 92450u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3698a2

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	3	-1	0	-1	3	-7	-3	-9	-7	11	6	+	0	-9	-12	-1	5	3	11	-1	-15	-9	-10

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Quadratic twists for elliptic curve 3698a2

-4	8	-3	5	-43
29584j2	118336f2	33282y2	92450u2	3698b2

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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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