Cremona's table of elliptic curves

3690 = 2 · 3² · 5 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 41+	Signs for the Atkin-Lehner involutions
Class	3690q	Isogeny class
Conductor	3690	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	47822400 = 26 · 36 · 52 · 41	Discriminant
Eigenvalues	2- 3- 5+ -2  6 -2 -8 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-128,-413]	[a1,a2,a3,a4,a6]
Generators	[-7:13:1]	Generators of the group modulo torsion
j	315821241/65600	j-invariant
L	4.778570478666	L(r)(E,1)/r!
Ω	1.4410266245112	Real period
R	0.55268126179219	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	29520bj1 118080cd1 410a1 18450j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3690q1

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
-	-	+	-2	6	-2	-8	-6	0	8	0	-6	+	-4	-6	-2	-8	10	-8	4	-6	-8	4	2	12

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Quadratic twists for elliptic curve 3690q1

-4	8	-3	5
29520bj1	118080cd1	410a1	18450j1

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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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