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	2772g	Isogeny class
Conductor	2772	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-100590336 = -1 · 28 · 36 · 72 · 11	Discriminant
Eigenvalues	2- 3-  1 7+ 11+ -4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-192,-1132]	[a1,a2,a3,a4,a6]
Generators	[29:133:1]	Generators of the group modulo torsion
j	-4194304/539	j-invariant
L	3.3649871999427	L(r)(E,1)/r!
Ω	0.63670593877106	Real period
R	2.6424971050511	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	11088bx1 44352bj1 308a1 69300bu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2772g1

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	+	+	-4	6	-2	-1	-2	-1	-9	-6	8	8	-10	-1	-2	11	-11	-14	-14	-4	-13	-9

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Quadratic twists for elliptic curve 2772g1

-4	8	-3	5	-7	-11
11088bx1	44352bj1	308a1	69300bu1	19404p1	30492bf1

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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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