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	9912k	Isogeny class
Conductor	9912	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-20627310348288 = -1 · 211 · 310 · 72 · 592	Discriminant
Eigenvalues	2- 3+  0 7-  4  4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2688,225900]	[a1,a2,a3,a4,a6]
Generators	[-11:504:1]	Generators of the group modulo torsion
j	-1049163349250/10071928881	j-invariant
L	4.2179322367761	L(r)(E,1)/r!
Ω	0.58253796445537	Real period
R	3.6203067389089	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19824g2 79296ba2 29736h2 69384bb2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9912k2

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

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Quadratic twists for elliptic curve 9912k2

-4	8	-3	-7
19824g2	79296ba2	29736h2	69384bb2

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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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