Cremona's table of elliptic curves

20160 = 2⁶ · 3² · 5 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 7-	Signs for the Atkin-Lehner involutions
Class	20160w	Isogeny class
Conductor	20160	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	5927040000 = 210 · 33 · 54 · 73	Discriminant
Eigenvalues	2+ 3+ 5- 7- -2  2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1272,17064]	[a1,a2,a3,a4,a6]
Generators	[-2:140:1]	Generators of the group modulo torsion
j	8232302592/214375	j-invariant
L	5.8798242824714	L(r)(E,1)/r!
Ω	1.3426713163178	Real period
R	0.36493321255747	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	20160df1 2520m1 20160k1 100800j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20160w1

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	8	2	-8	-8	6	-6	-4	-4	0	-4	2	4	-6	-6	0	-16	-6	-14

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Quadratic twists for elliptic curve 20160w1

-4	8	-3	5
20160df1	2520m1	20160k1	100800j1

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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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