Cremona's table of elliptic curves

22800 = 2⁴ · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 19-	Signs for the Atkin-Lehner involutions
Class	22800cf	Isogeny class
Conductor	22800	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	-8664000000000 = -1 · 212 · 3 · 59 · 192	Discriminant
Eigenvalues	2- 3+ 5+ -2  2  4 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,592,141312]	[a1,a2,a3,a4,a6]
Generators	[-38:250:1]	Generators of the group modulo torsion
j	357911/135375	j-invariant
L	4.278239334332	L(r)(E,1)/r!
Ω	0.56964853229893	Real period
R	0.93878924717543	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1425g1 91200ht1 68400fl1 4560y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22800cf1

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

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Quadratic twists for elliptic curve 22800cf1

-4	8	-3	5
1425g1	91200ht1	68400fl1	4560y1

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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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