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
Δ	-1167051 = -1 · 3 · 733	Discriminant
Eigenvalues	0 3- -3 -4  0 -4  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-27,-85]	[a1,a2,a3,a4,a6]
Generators	[23:109:1]	Generators of the group modulo torsion
j	-2258403328/1167051	j-invariant
L	1.2803214991664	L(r)(E,1)/r!
Ω	1.0191720494802	Real period
R	0.41874562128458	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	3504r2 14016o2 657c2 5475a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 219b2

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 219b2

-4	8	-3	5	-7	-11	13	17	-19	-23	73
3504r2	14016o2	657c2	5475a2	10731b2	26499h2	37011d2	63291b2	79059e2	115851u2	15987e2

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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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