Cremona's table of elliptic curves

2223 = 3² · 13 · 19

Field	Data	Notes
Atkin-Lehner	3- 13- 19+	Signs for the Atkin-Lehner involutions
Class	2223d	Isogeny class
Conductor	2223	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	-189606339 = -1 · 310 · 132 · 19	Discriminant
Eigenvalues	0 3- -1 -3  3 13-  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-48,-675]	[a1,a2,a3,a4,a6]
Generators	[17:58:1]	Generators of the group modulo torsion
j	-16777216/260091	j-invariant
L	2.3516511820522	L(r)(E,1)/r!
Ω	0.76924452867353	Real period
R	0.76427296340585	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	35568cf1 741e1 55575g1 108927k1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2223d1

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
0	-	-1	-3	3	-	3	+	8	0	-6	4	2	-9	-3	-8	-8	-5	14	8	-9	-14	4	-14	0

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Quadratic twists for elliptic curve 2223d1

-4	-3	5	-7	13	-19
35568cf1	741e1	55575g1	108927k1	28899i1	42237a1

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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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