Cremona's table of elliptic curves

9912 = 2³ · 3 · 7 · 59

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 59+	Signs for the Atkin-Lehner involutions
Class	9912f	Isogeny class
Conductor	9912	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	-1474602964595712 = -1 · 210 · 320 · 7 · 59	Discriminant
Eigenvalues	2+ 3-  2 7+  4  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-10872,1894752]	[a1,a2,a3,a4,a6]
j	-138800820116452/1440041957613	j-invariant
L	4.074376012397	L(r)(E,1)/r!
Ω	0.4074376012397	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19824c4 79296c3 29736r3 69384f3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9912f4

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

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Quadratic twists for elliptic curve 9912f4

-4	8	-3	-7
19824c4	79296c3	29736r3	69384f3

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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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