Cremona's table of elliptic curves

82800 = 2⁴ · 3² · 5² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	82800ek	Isogeny class
Conductor	82800	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	148086144000000 = 213 · 37 · 56 · 232	Discriminant
Eigenvalues	2- 3- 5+ -2 -6  2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-113475,14701250]	[a1,a2,a3,a4,a6]
Generators	[265:-1800:1] [-215:5400:1]	Generators of the group modulo torsion
j	3463512697/3174	j-invariant
L	10.186547621526	L(r)(E,1)/r!
Ω	0.57557183568421	Real period
R	0.55306669547295	Regulator
r	2	Rank of the group of rational points
S	1.0000000000111	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10350j2 27600bi2 3312o2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 82800ek2

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	-6	2	0	0	-	-6	-8	0	-10	-12	8	2	-12	4	-12	0	10	6	-14	0	6

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Quadratic twists for elliptic curve 82800ek2

-4	-3	5
10350j2	27600bi2	3312o2

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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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