Cremona's table of elliptic curves

1984 = 2⁶ · 31

Field	Data	Notes
Atkin-Lehner	2+ 31-	Signs for the Atkin-Lehner involutions
Class	1984f	Isogeny class
Conductor	1984	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-31744 = -1 · 210 · 31	Discriminant
Eigenvalues	2+  2  3 -1  6 -2  6  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9,17]	[a1,a2,a3,a4,a6]
j	-87808/31	j-invariant
L	3.4883891405628	L(r)(E,1)/r!
Ω	3.4883891405628	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1984h1 124a1 17856bh1 49600z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1984f1

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	3	-1	6	-2	6	1	-6	0	-	10	-9	-8	0	0	3	10	4	-15	14	8	-6	12	-7

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Quadratic twists for elliptic curve 1984f1

-4	8	-3	5	-7	-31
1984h1	124a1	17856bh1	49600z1	97216l1	61504bb1

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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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