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	2	Product of Tamagawa factors cp
Δ	55025228222 = 2 · 317	Discriminant
Eigenvalues	2-  0 -2  0  0 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-317791,-68874615]	[a1,a2,a3,a4,a6]
Generators	[27497026964693456898474:3994045625106542444756791:1293368746198925304]	Generators of the group modulo torsion
j	3999236143617/62	j-invariant
L	3.7985906461558	L(r)(E,1)/r!
Ω	0.20107786412382	Real period
R	37.78228561068	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	15376u4 61504k4 17298i4 48050b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1922d3

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 1922d3

-4	8	-3	5	-7	-31
15376u4	61504k4	17298i4	48050b4	94178u4	62a4

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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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