Cremona's table of elliptic curves

12992 = 2⁶ · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 7- 29-	Signs for the Atkin-Lehner involutions
Class	12992bk	Isogeny class
Conductor	12992	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	-3325952 = -1 · 214 · 7 · 29	Discriminant
Eigenvalues	2-  1  0 7- -6 -4  6 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,27,-61]	[a1,a2,a3,a4,a6]
j	128000/203	j-invariant
L	1.3257963499746	L(r)(E,1)/r!
Ω	1.3257963499746	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12992g1 3248d1 116928ec1 90944dy1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12992bk1

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
-	1	0	-	-6	-4	6	-5	1	-	-8	8	-7	-10	5	11	0	-2	9	15	3	12	6	11	-1

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Quadratic twists for elliptic curve 12992bk1

-4	8	-3	-7
12992g1	3248d1	116928ec1	90944dy1

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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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