Cremona's table of elliptic curves

3933 = 3² · 19 · 23

Field	Data	Notes
Atkin-Lehner	3- 19- 23-	Signs for the Atkin-Lehner involutions
Class	3933f	Isogeny class
Conductor	3933	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-214254041139 = -1 · 310 · 193 · 232	Discriminant
Eigenvalues	2 3-  3  1 -1  0  5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,159,-22257]	[a1,a2,a3,a4,a6]
j	609800192/293901291	j-invariant
L	5.6076873967606	L(r)(E,1)/r!
Ω	0.46730728306338	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	62928y1 1311d1 98325bo1 74727s1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 3933f1

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	-1	0	5	-	-	4	4	8	-2	1	3	0	6	-3	-10	16	1	4	12	-8	-16

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Quadratic twists for elliptic curve 3933f1

-4	-3	5	-19	-23
62928y1	1311d1	98325bo1	74727s1	90459n1

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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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