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	22800cc	Isogeny class
Conductor	22800	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	205200 = 24 · 33 · 52 · 19	Discriminant
Eigenvalues	2- 3+ 5+ -1  0  0 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-18,27]	[a1,a2,a3,a4,a6]
Generators	[1:3:1]	Generators of the group modulo torsion
j	1703680/513	j-invariant
L	4.1335530320993	L(r)(E,1)/r!
Ω	2.9391918008842	Real period
R	1.4063570233341	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5700k1 91200ho1 68400fd1 22800dr1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22800cc1

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
-	+	+	-1	0	0	-2	-	4	-5	8	-2	-7	12	-6	-3	-5	-1	10	-15	9	4	-2	5	12

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Quadratic twists for elliptic curve 22800cc1

-4	8	-3	5
5700k1	91200ho1	68400fd1	22800dr1

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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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