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	20160db	Isogeny class
Conductor	20160	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	215040	Modular degree for the optimal curve
Δ	9745044571422720 = 232 · 33 · 5 · 75	Discriminant
Eigenvalues	2- 3+ 5+ 7- -4 -6  4  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-327948,-72130032]	[a1,a2,a3,a4,a6]
Generators	[-324:336:1]	Generators of the group modulo torsion
j	551105805571803/1376829440	j-invariant
L	4.5066969875012	L(r)(E,1)/r!
Ω	0.19953243897415	Real period
R	2.258628727575	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	20160e1 5040bb1 20160dm1 100800jk1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20160db1

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	-6	4	6	0	6	4	-8	10	-2	-10	-14	-4	8	6	2	-10	-16	-8	2	2

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Quadratic twists for elliptic curve 20160db1

-4	8	-3	5
20160e1	5040bb1	20160dm1	100800jk1

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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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