Cremona's table of elliptic curves

2772 = 2² · 3² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	2772c	Isogeny class
Conductor	2772	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-1629936 = -1 · 24 · 33 · 73 · 11	Discriminant
Eigenvalues	2- 3+ -3 7- 11+  5 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-69,229]	[a1,a2,a3,a4,a6]
Generators	[-4:21:1]	Generators of the group modulo torsion
j	-84098304/3773	j-invariant
L	2.88297300922	L(r)(E,1)/r!
Ω	2.641140018469	Real period
R	0.54578193300241	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	11088ba1 44352n1 2772d2 69300c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2772c1

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	-	+	5	-6	-1	0	9	8	-7	-6	-10	-3	-6	9	2	-13	-6	11	-10	6	-6	-10

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Quadratic twists for elliptic curve 2772c1

-4	8	-3	5	-7	-11
11088ba1	44352n1	2772d2	69300c1	19404c1	30492d1

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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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