Cremona's table of elliptic curves

219 = 3 · 73

Field	Data	Notes
Atkin-Lehner	3- 73-	Signs for the Atkin-Lehner involutions
Class	219b	Isogeny class
Conductor	219	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	-1971 = -1 · 33 · 73	Discriminant
Eigenvalues	0 3- -3 -4  0 -4  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,3,2]	[a1,a2,a3,a4,a6]
Generators	[2:4:1]	Generators of the group modulo torsion
j	2097152/1971	j-invariant
L	1.2803214991664	L(r)(E,1)/r!
Ω	3.0575161484406	Real period
R	1.2562368638538	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	3504r1 14016o1 657c1 5475a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 219b1

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	-	-3	-4	0	-4	3	-1	6	-6	-10	-7	0	2	-3	9	-9	-1	-13	12	-	11	15	-18	5

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Quadratic twists for elliptic curve 219b1

-4	8	-3	5	-7	-11	13	17	-19	-23	73
3504r1	14016o1	657c1	5475a1	10731b1	26499h1	37011d1	63291b1	79059e1	115851u1	15987e1

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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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