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	22320g	Isogeny class
Conductor	22320	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	1452699878400 = 210 · 310 · 52 · 312	Discriminant
Eigenvalues	2+ 3- 5+  0  0 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3963,76538]	[a1,a2,a3,a4,a6]
Generators	[-59:324:1]	Generators of the group modulo torsion
j	9220796644/1946025	j-invariant
L	4.3827279865161	L(r)(E,1)/r!
Ω	0.80474251537949	Real period
R	1.3615311428058	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	11160c2 89280fn2 7440d2 111600be2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22320g2

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
+	-	+	0	0	-2	-6	-4	4	-2	-	-2	6	4	0	10	12	10	-4	0	14	8	12	-10	10

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Quadratic twists for elliptic curve 22320g2

-4	8	-3	5
11160c2	89280fn2	7440d2	111600be2

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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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