Cremona's table of elliptic curves

22080 = 2⁶ · 3 · 5 · 23

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 23+	Signs for the Atkin-Lehner involutions
Class	22080f	Isogeny class
Conductor	22080	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16128	Modular degree for the optimal curve
Δ	9936000000 = 210 · 33 · 56 · 23	Discriminant
Eigenvalues	2+ 3+ 5+ -4  0 -2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-661,-4235]	[a1,a2,a3,a4,a6]
Generators	[29:12:1]	Generators of the group modulo torsion
j	31238127616/9703125	j-invariant
L	2.9448739210942	L(r)(E,1)/r!
Ω	0.96432807362317	Real period
R	3.0538091772334	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	22080cs1 1380d1 66240dg1 110400ei1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22080f1

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

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Quadratic twists for elliptic curve 22080f1

-4	8	-3	5
22080cs1	1380d1	66240dg1	110400ei1

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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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