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	4	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	29584 = 24 · 432	Discriminant
Eigenvalues	2- -1 -3  1  0 -1  3  7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-17,-33]	[a1,a2,a3,a4,a6]
Generators	[-3:2:1]	Generators of the group modulo torsion
j	294937/16	j-invariant
L	3.7419733159035	L(r)(E,1)/r!
Ω	2.3584092074557	Real period
R	0.39666285478298	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	29584l1 118336m1 33282o1 92450f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3698b1

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 3698b1

-4	8	-3	5	-43
29584l1	118336m1	33282o1	92450f1	3698a1

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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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