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	40800bg	Isogeny class
Conductor	40800	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	26880	Modular degree for the optimal curve
Δ	-29376000000 = -1 · 212 · 33 · 56 · 17	Discriminant
Eigenvalues	2- 3+ 5+  2 -1  1 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3533,82437]	[a1,a2,a3,a4,a6]
j	-76225024/459	j-invariant
L	2.3692905844626	L(r)(E,1)/r!
Ω	1.1846452922218	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40800bq1 81600hy1 122400bd1 1632e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 40800bg1

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
-	+	+	2	-1	1	+	1	5	2	-2	8	5	5	12	0	-2	2	4	-8	0	-6	4	6	2

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Quadratic twists for elliptic curve 40800bg1

-4	8	-3	5
40800bq1	81600hy1	122400bd1	1632e1

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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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