Cremona's table of elliptic curves

1424 = 2⁴ · 89

Field	Data	Notes
Atkin-Lehner	2- 89+	Signs for the Atkin-Lehner involutions
Class	1424b	Isogeny class
Conductor	1424	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-364544 = -1 · 212 · 89	Discriminant
Eigenvalues	2-  1 -1  4  2  2  3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-16,-44]	[a1,a2,a3,a4,a6]
j	-117649/89	j-invariant
L	2.2993520441949	L(r)(E,1)/r!
Ω	1.1496760220975	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	89a1 5696j1 12816l1 35600t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1424b1

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	-1	4	2	2	3	5	-7	0	9	-2	0	7	12	-3	-4	6	-12	10	7	6	-12	+	9

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Quadratic twists for elliptic curve 1424b1

-4	8	-3	5	-7	89
89a1	5696j1	12816l1	35600t1	69776z1	126736f1

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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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