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	40800f	Isogeny class
Conductor	40800	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	18360000000000 = 212 · 33 · 510 · 17	Discriminant
Eigenvalues	2+ 3+ 5+  0  0  2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-62033,5963937]	[a1,a2,a3,a4,a6]
j	412495384384/286875	j-invariant
L	1.3653115144055	L(r)(E,1)/r!
Ω	0.68265575723145	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	40800bs4 81600dk1 122400ct4 8160m3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 40800f4

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

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Quadratic twists for elliptic curve 40800f4

-4	8	-3	5
40800bs4	81600dk1	122400ct4	8160m3

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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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