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	22320bi	Isogeny class
Conductor	22320	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	948941049600 = 28 · 314 · 52 · 31	Discriminant
Eigenvalues	2- 3- 5+  2 -4 -4  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2703,27002]	[a1,a2,a3,a4,a6]
Generators	[-2:180:1]	Generators of the group modulo torsion
j	11702923216/5084775	j-invariant
L	4.6476185379908	L(r)(E,1)/r!
Ω	0.79475131094772	Real period
R	2.9239451850974	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	5580e2 89280ff2 7440m2 111600ec2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22320bi2

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	-4	-4	0	0	0	6	+	-8	10	4	10	0	-4	-6	2	8	4	-16	-4	18	14

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Quadratic twists for elliptic curve 22320bi2

-4	8	-3	5
5580e2	89280ff2	7440m2	111600ec2

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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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