Cremona's table of elliptic curves

3698 = 2 · 43²

Field	Data	Notes
Atkin-Lehner	2- 43-	Signs for the Atkin-Lehner involutions
Class	3698b	Isogeny class
Conductor	3698	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	7573504 = 212 · 432	Discriminant
Eigenvalues	2- -1 -3  1  0 -1  3  7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-232,1257]	[a1,a2,a3,a4,a6]
Generators	[5:13:1]	Generators of the group modulo torsion
j	747081097/4096	j-invariant
L	3.7419733159035	L(r)(E,1)/r!
Ω	2.3584092074557	Real period
R	0.13222095159433	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	29584l2 118336m2 33282o2 92450f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3698b2

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 3698b2

-4	8	-3	5	-43
29584l2	118336m2	33282o2	92450f2	3698a2

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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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