Cremona's table of elliptic curves

3333 = 3 · 11 · 101

Field	Data	Notes
Atkin-Lehner	3+ 11+ 101-	Signs for the Atkin-Lehner involutions
Class	3333b	Isogeny class
Conductor	3333	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	704	Modular degree for the optimal curve
Δ	109989 = 32 · 112 · 101	Discriminant
Eigenvalues	-2 3+ -3 -2 11+ -5  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-52,162]	[a1,a2,a3,a4,a6]
Generators	[-5:16:1] [1:10:1]	Generators of the group modulo torsion
j	15851081728/109989	j-invariant
L	1.7650984817607	L(r)(E,1)/r!
Ω	3.3556282286448	Real period
R	0.13150283355985	Regulator
r	2	Rank of the group of rational points
S	0.99999999999993	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53328y1 9999m1 83325p1 36663c1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3333b1

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	-2	+	-5	3	1	-5	0	-9	-2	-6	-4	5	-4	0	-14	0	-9	6	-15	-6	-10	-14

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Quadratic twists for elliptic curve 3333b1

-4	-3	5	-11
53328y1	9999m1	83325p1	36663c1

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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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