Cremona's table of elliptic curves

19220 = 2² · 5 · 31²

Field	Data	Notes
Atkin-Lehner	2- 5+ 31-	Signs for the Atkin-Lehner involutions
Class	19220b	Isogeny class
Conductor	19220	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1775007362000 = 24 · 53 · 316	Discriminant
Eigenvalues	2-  2 5+  2  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-39721,3059646]	[a1,a2,a3,a4,a6]
Generators	[-2379972:54128325:21952]	Generators of the group modulo torsion
j	488095744/125	j-invariant
L	7.1592655890354	L(r)(E,1)/r!
Ω	0.81690425486511	Real period
R	8.7638980289282	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	76880s3 96100g3 20a4	Quadratic twists by: -4 5 -31

Hecke Eigenvalues for elliptic curve 19220b3

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

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Quadratic twists for elliptic curve 19220b3

-4	5	-31
76880s3	96100g3	20a4

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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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