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	8	Product of Tamagawa factors cp
Δ	3411564149764 = 22 · 318	Discriminant
Eigenvalues	2-  0 -2  0  0 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-19881,-1070299]	[a1,a2,a3,a4,a6]
Generators	[23228295805:3374899848614:1092727]	Generators of the group modulo torsion
j	979146657/3844	j-invariant
L	3.7985906461558	L(r)(E,1)/r!
Ω	0.40215572824764	Real period
R	18.89114280534	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	15376u2 61504k2 17298i2 48050b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1922d2

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 1922d2

-4	8	-3	5	-7	-31
15376u2	61504k2	17298i2	48050b2	94178u2	62a2

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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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