Cremona's table of elliptic curves

28560 = 2⁴ · 3 · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7- 17-	Signs for the Atkin-Lehner involutions
Class	28560bz	Isogeny class
Conductor	28560	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	122880	Modular degree for the optimal curve
Δ	887932631250000 = 24 · 35 · 58 · 7 · 174	Discriminant
Eigenvalues	2+ 3- 5- 7-  4 -2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-60775,5565548]	[a1,a2,a3,a4,a6]
Generators	[56:1530:1]	Generators of the group modulo torsion
j	1551621461335545856/55495789453125	j-invariant
L	7.9712064949194	L(r)(E,1)/r!
Ω	0.49524635391802	Real period
R	0.40238592530046	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	14280k1 114240gm1 85680bg1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 28560bz1

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

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Quadratic twists for elliptic curve 28560bz1

-4	8	-3
14280k1	114240gm1	85680bg1

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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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