Cremona's table of elliptic curves

81600 = 2⁶ · 3 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	81600ih	Isogeny class
Conductor	81600	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	440640000000000 = 215 · 34 · 510 · 17	Discriminant
Eigenvalues	2- 3- 5+ -4  4 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-25633,-1223137]	[a1,a2,a3,a4,a6]
Generators	[-97:600:1]	Generators of the group modulo torsion
j	3638052872/860625	j-invariant
L	5.925909025982	L(r)(E,1)/r!
Ω	0.383771486981	Real period
R	0.9650777265693	Regulator
r	1	Rank of the group of rational points
S	0.99999999985457	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	81600fv4 40800e3 16320cg3	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 81600ih4

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	4	-6	+	0	-8	-2	-8	10	6	-4	8	-2	-4	6	-4	12	-14	8	16	18	10

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Quadratic twists for elliptic curve 81600ih4

-4	8	5
81600fv4	40800e3	16320cg3

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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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