Cremona's table of elliptic curves

1922 = 2 · 31²

Field	Data	Notes
Atkin-Lehner	2- 31-	Signs for the Atkin-Lehner involutions
Class	1922d	Isogeny class
Conductor	1922	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1639256573961602 = 2 · 3110	Discriminant
Eigenvalues	2-  0 -2  0  0 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-29491,79057]	[a1,a2,a3,a4,a6]
Generators	[-11006360:18635919:64000]	Generators of the group modulo torsion
j	3196010817/1847042	j-invariant
L	3.7985906461558	L(r)(E,1)/r!
Ω	0.40215572824764	Real period
R	9.4455714026701	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	15376u3 61504k3 17298i3 48050b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1922d4

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

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Quadratic twists for elliptic curve 1922d4

-4	8	-3	5	-7	-31
15376u3	61504k3	17298i3	48050b3	94178u3	62a3

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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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