Cremona's table of elliptic curves

6786 = 2 · 3² · 13 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 13- 29+	Signs for the Atkin-Lehner involutions
Class	6786f	Isogeny class
Conductor	6786	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-307742602752 = -1 · 29 · 313 · 13 · 29	Discriminant
Eigenvalues	2+ 3-  2 -2  1 13-  7 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2511,-54675]	[a1,a2,a3,a4,a6]
Generators	[453:9345:1]	Generators of the group modulo torsion
j	-2402335209457/422143488	j-invariant
L	3.3936312693076	L(r)(E,1)/r!
Ω	0.33400957867144	Real period
R	5.0801406396878	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	54288bq1 2262l1 88218bz1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 6786f1

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	-2	1	-	7	-2	0	+	-3	-10	-6	-11	-6	-3	0	-9	9	3	11	-4	2	6	-6

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Quadratic twists for elliptic curve 6786f1

-4	-3	13
54288bq1	2262l1	88218bz1

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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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