Cremona's table of elliptic curves

40800 = 2⁵ · 3 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	40800w	Isogeny class
Conductor	40800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	6885000000000 = 29 · 34 · 510 · 17	Discriminant
Eigenvalues	2+ 3- 5+  4  4  6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6408,149688]	[a1,a2,a3,a4,a6]
j	3638052872/860625	j-invariant
L	5.6239767037375	L(r)(E,1)/r!
Ω	0.70299708798021	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	40800e3 81600fv4 122400du3 8160i3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 40800w3

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 40800w3

-4	8	-3	5
40800e3	81600fv4	122400du3	8160i3

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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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