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	22800t	Isogeny class
Conductor	22800	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	84480	Modular degree for the optimal curve
Δ	-27702000000000 = -1 · 210 · 36 · 59 · 19	Discriminant
Eigenvalues	2+ 3+ 5-  4 -4  6  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8208,384912]	[a1,a2,a3,a4,a6]
Generators	[17:500:1]	Generators of the group modulo torsion
j	-30581492/13851	j-invariant
L	5.4367796706212	L(r)(E,1)/r!
Ω	0.62243480766338	Real period
R	2.1836743397396	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	11400r1 91200ix1 68400da1 22800bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22800t1

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
+	+	-	4	-4	6	2	-	6	-10	2	-6	-12	2	6	6	-14	-6	-8	-4	8	10	-16	-16	-14

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Quadratic twists for elliptic curve 22800t1

-4	8	-3	5
11400r1	91200ix1	68400da1	22800bp1

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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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