Cremona's table of elliptic curves

1922 = 2 · 31²

Field	Data	Notes
Atkin-Lehner	2+ 31+	Signs for the Atkin-Lehner involutions
Class	1922a	Isogeny class
Conductor	1922	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	3720	Modular degree for the optimal curve
Δ	3411564149764 = 22 · 318	Discriminant
Eigenvalues	2+  1 -3 -1  3  5  3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4345,64840]	[a1,a2,a3,a4,a6]
Generators	[119:1052:1]	Generators of the group modulo torsion
j	10633/4	j-invariant
L	2.2093451329891	L(r)(E,1)/r!
Ω	0.7238343355787	Real period
R	4.5784201392355	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	15376r1 61504g1 17298p1 48050p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1922a1

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
+	1	-3	-1	3	5	3	-7	0	6	+	-7	3	5	-12	9	-3	-10	-13	-3	-13	-1	-9	6	2

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Quadratic twists for elliptic curve 1922a1

-4	8	-3	5	-7	-31
15376r1	61504g1	17298p1	48050p1	94178a1	1922b1

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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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