Cremona's table of elliptic curves

219 = 3 · 73

Field	Data	Notes
Atkin-Lehner	3+ 73+	Signs for the Atkin-Lehner involutions
Class	219c	Isogeny class
Conductor	219	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1294947 = 35 · 732	Discriminant
Eigenvalues	1 3+ -4  2 -4 -2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1297,-18530]	[a1,a2,a3,a4,a6]
Generators	[414:1691:8]	Generators of the group modulo torsion
j	241583200934041/1294947	j-invariant
L	1.4044028078577	L(r)(E,1)/r!
Ω	0.79546506177511	Real period
R	3.5310232349457	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	3504v2 14016u2 657a2 5475h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 219c2

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	+	-4	2	-4	-2	0	-4	0	8	6	-2	-10	-6	-8	-12	4	-14	8	-8	+	8	16	-14	-2

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Quadratic twists for elliptic curve 219c2

-4	8	-3	5	-7	-11	13	17	-19	-23	73
3504v2	14016u2	657a2	5475h2	10731f2	26499d2	37011b2	63291l2	79059l2	115851e2	15987c2

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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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