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	9912h	Isogeny class
Conductor	9912	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	79930368 = 210 · 33 · 72 · 59	Discriminant
Eigenvalues	2+ 3-  2 7- -4 -2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-512,4272]	[a1,a2,a3,a4,a6]
Generators	[4:48:1]	Generators of the group modulo torsion
j	14523844612/78057	j-invariant
L	5.9529320919771	L(r)(E,1)/r!
Ω	1.9378828128574	Real period
R	1.0239580454299	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	19824a1 79296l1 29736v1 69384g1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9912h1

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	0	-4	0	0	6	-12	0	2	-8	0	+	2	2	-4	4	0	-4	-2	-16

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Quadratic twists for elliptic curve 9912h1

-4	8	-3	-7
19824a1	79296l1	29736v1	69384g1

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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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