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	12992bb	Isogeny class
Conductor	12992	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-31193792 = -1 · 26 · 75 · 29	Discriminant
Eigenvalues	2- -1  4 7+  2 -4 -2  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,79,-17]	[a1,a2,a3,a4,a6]
Generators	[42:275:1]	Generators of the group modulo torsion
j	841232384/487403	j-invariant
L	4.7948710905337	L(r)(E,1)/r!
Ω	1.2506728045432	Real period
R	3.8338333360379	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12992r1 3248g1 116928do1 90944dv1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12992bb1

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	4	+	2	-4	-2	5	-9	-	8	-8	-3	-6	7	-9	0	-2	3	-7	-1	0	14	15	3

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Quadratic twists for elliptic curve 12992bb1

-4	8	-3	-7
12992r1	3248g1	116928do1	90944dv1

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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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