Cremona's table of elliptic curves

4489 = 67²

Field	Data	Notes
Atkin-Lehner	67+	Signs for the Atkin-Lehner involutions
Class	4489a	Isogeny class
Conductor	4489	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-27206534396294947 = -1 · 679	Discriminant
Eigenvalues	0  0  0  0  0  0 -1  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-33083930,-73244287055]	[a1,a2,a3,a4,a6]
Generators	[63896501611047491620675654807858:10956085084392718114395997318977993:2090745506172424414999081096]	Generators of the group modulo torsion
j	-147197952000	j-invariant
L	2.8995888576371	L(r)(E,1)/r!
Ω	0.031474967150666	Real period
R	46.061825001392	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	71824a2 40401e2 112225a2 4489a1	Quadratic twists by: -4 -3 5 -67

Hecke Eigenvalues for elliptic curve 4489a2

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	0	0	0	0	0	-1	3	5	7	0	-9	0	0	11	0	13	0	+	-4	-15	0	8	-17	0

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Quadratic twists for elliptic curve 4489a2

-4	-3	5	-67
71824a2	40401e2	112225a2	4489a1

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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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