Cremona's table of elliptic curves

6776 = 2³ · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	6776b	Isogeny class
Conductor	6776	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	9984	Modular degree for the optimal curve
Δ	-818107136 = -1 · 28 · 74 · 113	Discriminant
Eigenvalues	2+ -3 -3 7- 11+ -4 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1804,29524]	[a1,a2,a3,a4,a6]
Generators	[-30:238:1] [2574:111034:729]	Generators of the group modulo torsion
j	-1905527808/2401	j-invariant
L	3.1557729809985	L(r)(E,1)/r!
Ω	1.5837901947173	Real period
R	0.06226702626724	Regulator
r	2	Rank of the group of rational points
S	0.99999999999945	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13552a1 54208z1 60984cd1 47432e1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6776b1

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	-3	-	+	-4	-4	-8	-3	-4	5	11	0	-4	-4	-10	3	-12	-5	-9	-16	-8	12	-13	-3

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Quadratic twists for elliptic curve 6776b1

-4	8	-3	-7	-11
13552a1	54208z1	60984cd1	47432e1	6776d1

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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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