Cremona's table of elliptic curves

4489 = 67²

Field	Data	Notes
Atkin-Lehner	67-	Signs for the Atkin-Lehner involutions
Class	4489b	Isogeny class
Conductor	4489	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	22440	Modular degree for the optimal curve
Δ	-6060711605323 = -1 · 677	Discriminant
Eigenvalues	-2  2 -2  2  4 -2  3  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-55364,5033956]	[a1,a2,a3,a4,a6]
j	-207474688/67	j-invariant
L	1.4806782240917	L(r)(E,1)/r!
Ω	0.74033911204587	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	71824e1 40401o1 112225f1 67a1	Quadratic twists by: -4 -3 5 -67

Hecke Eigenvalues for elliptic curve 4489b1

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
-2	2	-2	2	4	-2	3	7	9	-5	10	-1	0	2	-1	-10	9	2	-	0	-7	8	4	7	0

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Quadratic twists for elliptic curve 4489b1

-4	-3	5	-67
71824e1	40401o1	112225f1	67a1

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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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