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	6786k	Isogeny class
Conductor	6786	Conductor
∏ cp	144	Product of Tamagawa factors cp
Δ	8.0944879956047E+20	Discriminant
Eigenvalues	2- 3-  0  0  4 13+ -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-163470830,804507222269]	[a1,a2,a3,a4,a6]
Generators	[7353:499:1]	Generators of the group modulo torsion
j	662700021090401442944265625/1110355006255792128	j-invariant
L	6.1825404960276	L(r)(E,1)/r!
Ω	0.13578905643511	Real period
R	1.2647354691859	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	54288be2 2262e2 88218m2	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 6786k2

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	0	4	+	-2	-6	-8	+	-2	-4	2	0	12	-2	-6	-14	-8	-10	12	-4	6	14	-12

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Quadratic twists for elliptic curve 6786k2

-4	-3	13
54288be2	2262e2	88218m2

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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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