Cremona's table of elliptic curves

8160 = 2⁵ · 3 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 17+	Signs for the Atkin-Lehner involutions
Class	8160j	Isogeny class
Conductor	8160	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	221085000000000 = 29 · 32 · 510 · 173	Discriminant
Eigenvalues	2- 3+ 5-  2  0  4 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-49280,-4133100]	[a1,a2,a3,a4,a6]
Generators	[-140:50:1]	Generators of the group modulo torsion
j	25850840101954568/431806640625	j-invariant
L	4.2892252507416	L(r)(E,1)/r!
Ω	0.32075326346431	Real period
R	1.3372351085116	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	8160p2 16320ck2 24480j2 40800ba2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8160j2

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

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Quadratic twists for elliptic curve 8160j2

-4	8	-3	5
8160p2	16320ck2	24480j2	40800ba2

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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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