Cremona's table of elliptic curves

12054 = 2 · 3 · 7² · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 41+	Signs for the Atkin-Lehner involutions
Class	12054bb	Isogeny class
Conductor	12054	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	3139764275844 = 22 · 34 · 78 · 412	Discriminant
Eigenvalues	2- 3+ -2 7-  0 -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-84379,-9468859]	[a1,a2,a3,a4,a6]
Generators	[8023:714196:1]	Generators of the group modulo torsion
j	564727473247393/26687556	j-invariant
L	4.8540280186939	L(r)(E,1)/r!
Ω	0.28011874103886	Real period
R	8.6642328904735	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	96432cn2 36162bf2 1722o2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12054bb2

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	-	0	-6	-2	4	0	2	8	6	+	4	8	-6	0	-10	8	8	6	-16	0	-10	-2

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Quadratic twists for elliptic curve 12054bb2

-4	-3	-7
96432cn2	36162bf2	1722o2

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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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