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	3690k	Isogeny class
Conductor	3690	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-3586680 = -1 · 23 · 37 · 5 · 41	Discriminant
Eigenvalues	2+ 3- 5-  3 -2 -4  0  3	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-189,1053]	[a1,a2,a3,a4,a6]
Generators	[9:0:1]	Generators of the group modulo torsion
j	-1027243729/4920	j-invariant
L	2.9756885517039	L(r)(E,1)/r!
Ω	2.5095832370218	Real period
R	0.2964325418466	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	29520ca1 118080bb1 1230j1 18450bq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3690k1

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
+	-	-	3	-2	-4	0	3	-3	-10	-5	3	+	-11	8	-9	3	-8	-4	-4	2	0	-8	-3	-6

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Quadratic twists for elliptic curve 3690k1

-4	8	-3	5
29520ca1	118080bb1	1230j1	18450bq1

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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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