Cremona's table of elliptic curves

69966 = 2 · 3² · 13² · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 23-	Signs for the Atkin-Lehner involutions
Class	69966w	Isogeny class
Conductor	69966	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-26866944 = -1 · 28 · 33 · 132 · 23	Discriminant
Eigenvalues	2- 3+  3  0 -4 13+ -2 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-71,-321]	[a1,a2,a3,a4,a6]
Generators	[11:6:1]	Generators of the group modulo torsion
j	-8560539/5888	j-invariant
L	11.867082369891	L(r)(E,1)/r!
Ω	0.79887422004803	Real period
R	0.92842230914428	Regulator
r	1	Rank of the group of rational points
S	1.0000000000342	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69966b1 69966c1	Quadratic twists by: -3 13

Hecke Eigenvalues for elliptic curve 69966w1

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
-	+	3	0	-4	+	-2	-5	-	0	10	0	-2	-1	-9	-1	9	8	1	9	-6	-1	0	13	0

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Quadratic twists for elliptic curve 69966w1

-3	13
69966b1	69966c1

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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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