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	6786s	Isogeny class
Conductor	6786	Conductor
∏ cp	264	Product of Tamagawa factors cp
deg	12672	Modular degree for the optimal curve
Δ	-18461179017216 = -1 · 211 · 37 · 132 · 293	Discriminant
Eigenvalues	2- 3-  1  1 -2 13- -5  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1562,208473]	[a1,a2,a3,a4,a6]
Generators	[227:3279:1]	Generators of the group modulo torsion
j	-577801395289/25323976704	j-invariant
L	6.4809587452783	L(r)(E,1)/r!
Ω	0.5719808385797	Real period
R	0.042919420547925	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	54288bx1 2262b1 88218z1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 6786s1

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
-	-	1	1	-2	-	-5	1	-6	-	-10	-5	-11	1	1	-2	-7	10	2	-4	-4	2	12	10	4

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Quadratic twists for elliptic curve 6786s1

-4	-3	13
54288bx1	2262b1	88218z1

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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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