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
deg	14448	Modular degree for the optimal curve
Δ	187011204441616 = 24 · 438	Discriminant
Eigenvalues	2+  1  3 -1  0 -1  3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-31472,2043118]	[a1,a2,a3,a4,a6]
Generators	[-8701:1999557:1331]	Generators of the group modulo torsion
j	294937/16	j-invariant
L	3.4650598460247	L(r)(E,1)/r!
Ω	0.55981972953236	Real period
R	9.2843990571372	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	29584j1 118336f1 33282y1 92450u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3698a1

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 3698a1

-4	8	-3	5	-43
29584j1	118336f1	33282y1	92450u1	3698b1

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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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