Cremona's table of elliptic curves

6936 = 2³ · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3+ 17-	Signs for the Atkin-Lehner involutions
Class	6936k	Isogeny class
Conductor	6936	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	14688	Modular degree for the optimal curve
Δ	-48216435432192 = -1 · 28 · 33 · 178	Discriminant
Eigenvalues	2- 3+  0 -3  2 -3 17-  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8188,441988]	[a1,a2,a3,a4,a6]
Generators	[-96:578:1]	Generators of the group modulo torsion
j	-34000/27	j-invariant
L	3.0950410591475	L(r)(E,1)/r!
Ω	0.58341623574003	Real period
R	0.44208589419034	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	13872q1 55488bw1 20808q1 6936l1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 6936k1

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
-	+	0	-3	2	-3	-	1	4	-6	7	11	6	-1	-8	4	-6	3	5	0	2	-4	-8	-2	-3

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Quadratic twists for elliptic curve 6936k1

-4	8	-3	17
13872q1	55488bw1	20808q1	6936l1

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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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