Cremona's table of elliptic curves

22320 = 2⁴ · 3² · 5 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 31-	Signs for the Atkin-Lehner involutions
Class	22320r	Isogeny class
Conductor	22320	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-24211664640 = -1 · 28 · 39 · 5 · 312	Discriminant
Eigenvalues	2+ 3- 5-  2  0  4  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,33,7486]	[a1,a2,a3,a4,a6]
j	21296/129735	j-invariant
L	3.7706697760969	L(r)(E,1)/r!
Ω	0.94266744402424	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11160o1 89280es1 7440g1 111600bo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22320r1

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

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Quadratic twists for elliptic curve 22320r1

-4	8	-3	5
11160o1	89280es1	7440g1	111600bo1

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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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