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	2772m	Isogeny class
Conductor	2772	Conductor
∏ cp	108	Product of Tamagawa factors cp
Δ	-15975002736 = -1 · 24 · 37 · 73 · 113	Discriminant
Eigenvalues	2- 3- -3 7- 11- -1  0  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-489,7369]	[a1,a2,a3,a4,a6]
Generators	[-19:99:1]	Generators of the group modulo torsion
j	-1108671232/1369599	j-invariant
L	2.8852704669046	L(r)(E,1)/r!
Ω	1.1209775245278	Real period
R	0.2144906568726	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	11088bi2 44352cg2 924g2 69300bf2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2772m2

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	-	-	-1	0	5	-6	3	-4	-7	12	2	-3	-6	-3	2	-1	-12	-7	-4	0	-6	2

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Quadratic twists for elliptic curve 2772m2

-4	8	-3	5	-7	-11
11088bi2	44352cg2	924g2	69300bf2	19404ba2	30492u2

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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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