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	22320bg	Isogeny class
Conductor	22320	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	24000	Modular degree for the optimal curve
Δ	-289267200000 = -1 · 212 · 36 · 55 · 31	Discriminant
Eigenvalues	2- 3- 5+  2  2 -6  7  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1392,16432]	[a1,a2,a3,a4,a6]
Generators	[16203:397709:27]	Generators of the group modulo torsion
j	99897344/96875	j-invariant
L	5.5201676811672	L(r)(E,1)/r!
Ω	0.63985163396124	Real period
R	8.6272619903969	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	1395c1 89280fd1 2480m1 111600dy1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22320bg1

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	-6	7	5	4	0	+	-7	3	-9	-2	-9	-5	-8	-8	-3	-1	0	-11	-10	18

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Quadratic twists for elliptic curve 22320bg1

-4	8	-3	5
1395c1	89280fd1	2480m1	111600dy1

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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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