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	40800ba	Isogeny class
Conductor	40800	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	3454453125000000000 = 29 · 32 · 516 · 173	Discriminant
Eigenvalues	2+ 3- 5+ -2  0 -4 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1232008,-519101512]	[a1,a2,a3,a4,a6]
Generators	[-698:1122:1]	Generators of the group modulo torsion
j	25850840101954568/431806640625	j-invariant
L	6.2518242337025	L(r)(E,1)/r!
Ω	0.14344522022222	Real period
R	3.631946411328	Regulator
r	1	Rank of the group of rational points
S	1.0000000000006	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	40800g2 81600go2 122400cz2 8160j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 40800ba2

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

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Quadratic twists for elliptic curve 40800ba2

-4	8	-3	5
40800g2	81600go2	122400cz2	8160j2

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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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