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	40800a	Isogeny class
Conductor	40800	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	6013512000000 = 29 · 32 · 56 · 174	Discriminant
Eigenvalues	2+ 3+ 5+  0  4  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4808,-48888]	[a1,a2,a3,a4,a6]
Generators	[-27:246:1]	Generators of the group modulo torsion
j	1536800264/751689	j-invariant
L	5.165876116148	L(r)(E,1)/r!
Ω	0.60244930467902	Real period
R	4.2873948695992	Regulator
r	1	Rank of the group of rational points
S	0.99999999999983	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	40800s3 81600hv3 122400dm3 1632l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 40800a3

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

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Quadratic twists for elliptic curve 40800a3

-4	8	-3	5
40800s3	81600hv3	122400dm3	1632l2

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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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