Cremona's table of elliptic curves

2277 = 3² · 11 · 23

Field	Data	Notes
Atkin-Lehner	3- 11+ 23-	Signs for the Atkin-Lehner involutions
Class	2277b	Isogeny class
Conductor	2277	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	32347398219543 = 38 · 118 · 23	Discriminant
Eigenvalues	1 3-  2  0 11+ -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-12681,-473526]	[a1,a2,a3,a4,a6]
Generators	[160110:1177461:1000]	Generators of the group modulo torsion
j	309368403125137/44372288367	j-invariant
L	4.0485242827885	L(r)(E,1)/r!
Ω	0.45419439066289	Real period
R	8.9136377859702	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	36432cb3 759b4 56925m3 111573bd3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2277b3

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	-	2	0	+	-2	-2	-4	-	2	0	-10	6	-12	0	-14	4	6	-4	8	-6	8	-4	14	2

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Quadratic twists for elliptic curve 2277b3

-4	-3	5	-7	-11	-23
36432cb3	759b4	56925m3	111573bd3	25047i3	52371d3

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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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