Cremona's table of elliptic curves

66309 = 3 · 23 · 31²

Field	Data	Notes
Atkin-Lehner	3+ 23- 31-	Signs for the Atkin-Lehner involutions
Class	66309f	Isogeny class
Conductor	66309	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	207360	Modular degree for the optimal curve
Δ	-17085333362931 = -1 · 33 · 23 · 317	Discriminant
Eigenvalues	2 3+  1  0 -2 -4  4  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-320,198989]	[a1,a2,a3,a4,a6]
Generators	[-43790:356031:1000]	Generators of the group modulo torsion
j	-4096/19251	j-invariant
L	10.913632775255	L(r)(E,1)/r!
Ω	0.55589851401949	Real period
R	4.9081048520843	Regulator
r	1	Rank of the group of rational points
S	0.999999999959	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2139d1	Quadratic twists by: -31

Hecke Eigenvalues for elliptic curve 66309f1

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	+	1	0	-2	-4	4	8	-	-9	-	-3	10	8	4	-6	-14	14	14	-6	0	5	2	2	6

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Quadratic twists for elliptic curve 66309f1

-31
2139d1

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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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