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
deg	1292	Modular degree for the optimal curve
Δ	-300763 = -1 · 673	Discriminant
Eigenvalues	0  0  0  0  0  0 -1  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-7370,243528]	[a1,a2,a3,a4,a6]
Generators	[402:63:8]	Generators of the group modulo torsion
j	-147197952000	j-invariant
L	2.8995888576371	L(r)(E,1)/r!
Ω	2.1088227990946	Real period
R	0.6874899253939	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	71824a1 40401e1 112225a1 4489a2	Quadratic twists by: -4 -3 5 -67

Hecke Eigenvalues for elliptic curve 4489a1

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 4489a1

-4	-3	5	-67
71824a1	40401e1	112225a1	4489a2

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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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