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	6936d	Isogeny class
Conductor	6936	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-25526348169984 = -1 · 28 · 35 · 177	Discriminant
Eigenvalues	2+ 3+  3  4 -1 -5 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5009,280437]	[a1,a2,a3,a4,a6]
Generators	[-11:578:1]	Generators of the group modulo torsion
j	-2249728/4131	j-invariant
L	4.6018028466345	L(r)(E,1)/r!
Ω	0.59854157443496	Real period
R	0.96104494724923	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	13872n1 55488br1 20808bg1 408d1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 6936d1

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	4	-1	-5	+	-7	-1	-2	6	-8	-7	-1	-6	-2	-10	-8	-12	-12	14	-10	-14	8	-12

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Quadratic twists for elliptic curve 6936d1

-4	8	-3	17
13872n1	55488br1	20808bg1	408d1

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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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