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	8	Product of Tamagawa factors cp
deg	1024	Modular degree for the optimal curve
Δ	-13311002727 = -1 · 314 · 112 · 23	Discriminant
Eigenvalues	1 3-  2  0 11+ -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,279,5184]	[a1,a2,a3,a4,a6]
Generators	[0:72:1]	Generators of the group modulo torsion
j	3288008303/18259263	j-invariant
L	4.0485242827885	L(r)(E,1)/r!
Ω	0.90838878132578	Real period
R	2.2284094464926	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	36432cb1 759b1 56925m1 111573bd1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2277b1

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

---

Quadratic twists for elliptic curve 2277b1

-4	-3	5	-7	-11	-23
36432cb1	759b1	56925m1	111573bd1	25047i1	52371d1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations