Cremona's table of elliptic curves

69312 = 2⁶ · 3 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3+ 19-	Signs for the Atkin-Lehner involutions
Class	69312cm	Isogeny class
Conductor	69312	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1015087726158938112 = 220 · 3 · 199	Discriminant
Eigenvalues	2- 3+  0  4  0 -4  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9888993,-11966111871]	[a1,a2,a3,a4,a6]
Generators	[6310850253189505534882405:649397180655349223272303744:547017700161650468633]	Generators of the group modulo torsion
j	8671983378625/82308	j-invariant
L	6.6248220119116	L(r)(E,1)/r!
Ω	0.085135713673094	Real period
R	38.907420433606	Regulator
r	1	Rank of the group of rational points
S	1.0000000000488	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69312bo3 17328be3 3648bh3	Quadratic twists by: -4 8 -19

Hecke Eigenvalues for elliptic curve 69312cm3

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
-	+	0	4	0	-4	6	-	6	6	2	-4	-6	-4	-6	6	12	-14	-8	0	14	-10	-12	6	10

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Quadratic twists for elliptic curve 69312cm3

-4	8	-19
69312bo3	17328be3	3648bh3

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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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